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300 (number)

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← 299 300 301 →
Cardinalthree hundred
Ordinal300th
(three hundredth)
Factorization22 × 3 × 52
Greek numeralΤ´
Roman numeralCCC, ccc
Binary1001011002
Ternary1020103
Senary12206
Octal4548
Duodecimal21012
Hexadecimal12C16
Hebrewש
ArmenianՅ
Babylonian cuneiform𒐙
Egyptian hieroglyph𓍤

300 (three hundred) is the natural number following 299 and preceding 301.

In mathematics

[edit]

300 is a composite number and the 24th triangular number.[1] It is also a second hexagonal number.[2]

Integers from 301 to 399

[edit]

300s

[edit]

301

[edit]

301 = 7 × 43. It is a Stirling number of the second kind represented by {7/3} because there are 301 ways to organize 7 objects into 3 non-empty sets.[3] It is a happy number, meaning that infinitely taking the sum of the squares of its digits will eventually result in 1.[4] 301 is a lazy caterer number because it is the maximum number of pieces that can be made by cutting a circle with 24 cuts.[5] It is the sum of three consecutive primes: 301 = 97 + 101 + 103.

302

[edit]

302 = 2 × 151. 302 is a happy number because repeatedly taking the sum of the squares of the digits of 302 will eventually result in 1.[6] It is a nontotient number because it is an even number and phi(x)=302 has no solutions.[7] There are 302 prime partitions of 40 meaning that there are 302 ways to separate 40 into the sum of prime parts.[8]

303

[edit]

303 = 3 × 101. 303 is a semiprime number becauuse it has only 2 prime factors. It is a palindromic number. There are 303 compositions of 10 where they cannot be viewed as a stack.[9] There are 303 bipartite graphs with 8 vertices.[10][11]

304

[edit]

304 = 24 × 19. It is a primitive semiperfect number because it is a semiperfect number that is not divisible by any other semiperfect number.[12] It is an untouchable number because it is not equal to the sum of any number's proper divisors.[13] 304 is a nontotient number because it is an even number and phi(x) = 304 has no solution.[14] It is the sum of consecutive primes in two different ways:[15]

304 = 41+43+47+53+59+61 = 23+29+31+37+41+43+47+53.

305

[edit]

305 = 5 × 61. It is the fifth hexagonal prism number which is defined by (n+1)(3n2+3n+1).[16] It is the convolution of the first 7 primes with themselves.[17] It is the hypotenuse of two Pythagorean triples: 3052=2072+2242=1362+2732.[18][19]

306

[edit]

306 = 2 × 32 × 17. It is the 17th oblong number meaning that it is equal to 17*18.[20][21] It is an untouchable number meaning that it cannot be equal to the sum of proper factors in any number.[22][23] It is the sum of four consecutive primes (71+73+79+83).

There are 306 triangular numbers with 5 digits.[24]

307

[edit]

307 is an isolated (i.e., not twin) prime,[25] but because 309 is a semiprime, 307 is a Chen prime.[26][27] 307 is the third non-palindromic number to have a palindromic square. 3072=94249.[28]

307 is one of only 16 natural numbers for which the imaginary quadratic field has class number 3.[29]

There are 307 one-sided noniamonds meaning that it is the number of ways to organize 9 triangles with each one touching at least one other on the edge.[30]

There are 307 solid partitions of 7.[31]

308

[edit]

308 = 22 × 7 × 11. It is a nontotient,[32] a heptagonal pyramidal number,[33] and the sum of two consecutive primes (151 + 157).[34] It is the totient sum of the first 41 integers.[35]

309

[edit]

309 = 3 × 103. It is a Blum integer and a centered icosahedral number.[36]

310s

[edit]

310

[edit]

310 = 2 × 5 × 31. It is a sphenic number meaning that it has 3 prime factors.[37] It is a noncototient number because m − φ(m) = 310 has no solutions.[38] There are 310 Dyks 11 paths with strictly intersecting peaks.[39] The sum of the divisors of 310 is a perfect square.[40]

311

[edit]

311 is a twin prime with 313, an irregular prime,[41] an emirp, and a permutable prime with 113 and 131. It is an Eisenstein prime with no imaginary part and real part of the form and a Gaussian prime with no imaginary part and real part of the form .

It can be expressed as a sum of consecutive primes in four different ways: as a sum of three consecutive primes (101 + 103 + 107), as a sum of five consecutive primes (53 + 59 + 61 + 67 + 71), as a sum of seven consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59), and as a sum of eleven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

311 is a strictly non-palindromic number, as it is not palindromic in any base between base 2 and base 309.[42]

311 is the smallest positive integer d such that the imaginary quadratic field Q(√–d) has a class number of 19.[43]

4311 - 3311 is a prime number.[44]

For all integers n from 1 to 42, the value of 311 * log2(n) is within ¼ of an integer.[45]

312

[edit]

312 = 23 × 3 × 13. It is a Idoneal number[46] and a practical number. It is a semiperfect number, as it is equal to the sum of some or all of its divisors. It is a Harshad number, as it is divisible by the sum of its digits.[47] It is part of a Pythagorean triple.

313

[edit]

313 is a twin prime with 311, a Pythagorean prime,[48] a regular prime,[49] a truncatable prime,[50] a weakly prime in base 5, and a palindromic prime in both decimal and binary. It is also the smallest number which is a full full reptend prime[51] in base 10 but not in base 2 to 9. It is an index of a prime Lucas number,[52] a centered square number,[53] and a happy number.[54]

314

[edit]

314 = 2 × 157.It is a nontotient[55] and a squarefree semiprime.[56] It forms a Pythagorean triple with 170 and 264. It is also what the first three digits of π (pi) would look like if the decimal point was removed.[57]

315

[edit]

315 = 32 × 5 × 7. It is a rencontres number and a highly composite odd number.

316

[edit]

316 = 22 × 79. It is a centered triangular number,[58] a centered heptagonal number,[59][60] an Ulam number,[61] and a member of one Tetranacci sequence.[62] It appears in counting asymmetric polyominoes[63] and binary-matrix involutions.[64]

317

[edit]

317 is a Chen prime[65] and an Eisenstein prime with no imaginary part. It is one of the rare primes that is both right and left truncatable, that is, one can remove the rightmost or leftmost digit, resulting in 31 and 17 respectively, both of which are still prime.[66] It is one of only two 3-digit primes satisfying the equation as p:

2 p + p = q

where p and q are both prime.

317 is also a strictly non-palindromic number.[67]

317 is the telephone area code for the city of Indianapolis, Indiana, United States and its surrounding counties. Because of this, the city celebrates 317 Day on March 17 (3/17), which has become a major cultural event in the city.[68][69]

318

[edit]

318 is a sphenic number,[70] a nontotient[71] and the sum of 12 consecutive primes, 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.[72] There are 318 posets with 6 unlabeled elements.[73]

319

[edit]

319 = 11 × 29. It is a Smith number[74] and a happy number in base 10.[75] It cannot be represented as the sum of fewer than 19 fourth powers. It is the sum of three consecutive primes (103 + 107 + 109).[76]

320s

[edit]

320

[edit]

320 = 26 × 5 = (25) × (2 × 5). It is a Leyland number,[77] and the maximum determinant of a 10 by 10 matrix of zeros and ones.[78]

321

[edit]

321 = 3 × 107. It is a Delannoy number[79]

322

[edit]

322 = 2 × 7 × 23. It is a sphenic,[80] a nontotient, an untouchable number,[81] and a Lucas number.[82] It is also the first unprimeable number to end in 2.

323

[edit]

323 is a semiprime, and the product of two consecutive prime numbers (17 × 19). It is also the sum of nine consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53) and the sum of the 13 consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47)

323 is the eighth Motzkin number, , meaning there are 323 ways to draw non-intersecting chords between eight points on a circle.

323 is the first Lucas pseudoprime with parameters (P, Q) defined by Selfridge's method. Additionally, it is the first Fibonacci pseudoprime (Lucas pseudoprime with P = 1 and Q = -1).

324

[edit]

324 = 22 × 34 = 182. It is a regular number, an abundant number, a Nialpdrome,[83] an untouchable number, also called a nonaliquot number,[84] an ulam number,[85] a powerful number,[86] and is the totient sum of the first 32 integers.[87] It is also the largest possible product of positive integers with sum 16.[88] It is the sum of four consecutive primes (73 + 79 + 83 + 89).[76]

325

[edit]

325 = 52 × 13. It is the smallest number to be the sum of two squares in 3 different ways: 12 + 182, 62 + 172 and 102 + 152. It is the smallest (and only known) 3-hyperperfect number.[89][90]

326

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326 = 2 × 163. It is a nontotient, a noncototient,[91] an untouchable number,[81] and a lazy caterer number.[92] It is the sum of the 14 consecutive primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).[76]

327

[edit]

327 = 3 × 109. It is a perfect totient number.[93] There are 327 compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing.[94]

328

[edit]

328 = 23 × 41. It is a refactorable number.[95] It is the sum of the first fifteen primes (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).[96]

329

[edit]

329 = 7 × 47. It is a highly cototient number.[97] It is the sum of three consecutive primes (107 + 109 + 113).[76]

330s

[edit]

330

[edit]

330 = 2 × 3 × 5 × 11. It is a pentatope number (a binomial coefficient ),[98] a pentagonal number,[99] and a sparsely totient number.[100] It is sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67).[76]

331

[edit]

331 is a prime number,[76] a super-prime,[101] a cuban prime,[102] a lucky prime,[103] a centered pentagonal number,[104] a centered hexagonal number,[105] and a zero of Mertens function.[106] It is the sum of five consecutive primes (59 + 61 + 67 + 71 + 73).[76]

332

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332 = 22 × 83. It is a zero of Mertens function.[106]

333

[edit]

333 = 32 × 37. It is a zero of Mertens function[106] and a repdigit.[107]

2333 is the smallest power of two greater than a googol.

334

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334 = 2 × 167. It is a nontotient.

335

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335 = 5 × 67. There are 335 Lyndon words of length 12.[108]

336

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336 = 24 × 3 × 7. It is an untouchable number[81] and a largely composite number.[109] There are 336 partitions of 41 into prime parts.[110]

337

[edit]

337 is a prime number,[76] an emirp,[111] a permutable prime,[112] and a Chen prime.[113]

338

[edit]

338 = 2 × 132. It is a nontotient. There are 338 square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.[114]

339

[edit]

339 = 3 × 113. It is an Ulam number.[115]

340s

[edit]

340

[edit]

340 = 22 × 5 × 17. It is a noncototient[91] and a nontotient.

It is the sum of the first four powers of 4 (41 + 42 + 43 + 44), the sum of eight consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), and the sum of ten consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).[76]

There are 340 regions formed by drawing the line segments connecting any two of the 12 perimeter points of a 3 times 3 grid of squares (sequence A331452 in the OEIS) and (sequence A255011 in the OEIS). [clarification needed]

341

[edit]

341 is an octagonal number,[116] a centered cube number,[117] and a super-Poulet number.[118] It is a palindrome and repdigit in bases 2 (1010101012), 4 (111114), 8 (5258), 17 (13117) and 30 (BB30). It is the sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61).[76]

341 is the smallest Fermat pseudoprime; it is the least composite odd modulus m greater than the base b, that satisfies the Fermat property "bm−1 − 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.[119]

342

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342 = 2 × 32 × 19. It is a pronic number,[120] and an untouchable number.[81]

343

[edit]

343 = 73, the first nice Friedman number that is composite since 343 = (3 + 4)3.[121] It is the only known example of x2+x+1 = y3, in this case, x=18, y=7. It is z3 in a triplet (x,y,z) such that x5 + y2 = z3.

344

[edit]

344 = 23 × 43. It is an octahedral number,[122] a noncototient,[91] a refactorable number,[95] and the totient sum of the first 33 integers.[123]

345

[edit]

345 = 3 × 5 × 23. It is a sphenic number[80] and an idoneal number.[124]

346

[edit]

346 = 2 × 173. It is a Smith number[74] and a noncototient.[91]

347

[edit]

347 is a prime number,[76] an emirp,[125] a safe prime,[126] an Eisenstein prime with no imaginary part, a Chen prime,[113] a twin prime with 349,[127] a strictly non-palindromic number,[128] and a Friedman prime since 347 = 73 + 4.[129]

348

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348 = 22 × 3 × 29. It is a refactorable number.[95] It is the sum of four consecutive primes (79 + 83 + 89 + 97).[76]

349

[edit]

349 is a prime number,[76] a twin prime with 347,[130] and a lucky prime.[131] It is the sum of three consecutive primes (109 + 113 + 127).[76]

5349 - 4349 is a prime number.[132]

350s

[edit]

350

[edit]

350 = 2 × 52 × 7. It is a primitive semiperfect number[133] and a nontotient. A truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

350= , making 350 a stirling number of the second kind.

351

[edit]

351 = 33 × 13. It is a member of the Padovan sequence[134] and the 26th triangular number.[135] It is the sum of five consecutive primes (61 + 67 + 71 + 73 + 79).[76] There are 351 compositions of 15 into distinct parts.[136]

352

[edit]

352 = 25 × 11. It is a lazy caterer number[92] and the sum of two consecutive primes (173 + 179).[76] There are 352 n-Queens Problem solutions for n = 9.[137]

353

[edit]

354

[edit]

354 = 2 × 3 × 59 = 14 + 24 + 34 + 44.[138][139] It is a sphenic number[80] and a nontotient. It is also sum of absolute value of the coefficients of Conway's polynomial.[140]

355

[edit]

355 = 5 × 71. It is a Smith number[74] and a zero of Mertens function.[106] The cototient of 355 is 75,[141] where 75 is the product of its digits (3 x 5 x 5 = 75).

It is the numerator of, 355/113, the best simplified rational approximation of pi having a denominator of four digits or fewer, known as Milü.

356

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356 = 22 × 89. It is a zero of Mertens function.[106]

357

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357 = 3 × 7 × 17. It is a sphenic number.[80]

358

[edit]

358 = 2 × 179. It is a zero of Mertens function[106] and the sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71).[76] There are 358 ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.[142][better source needed]

359

[edit]

359 is an Eisenstein prime with no imaginary part[143] and a Chen prime.[144] It is a strictly non-palindromic number.[145]

360s

[edit]

360

[edit]

361

[edit]

361 = 192. 361 is a centered triangular number,[146] a centered octagonal number,[147] a centered decagonal number[148] and a member of the Mian–Chowla sequence.[149] There are 361 intersections on a standard 19 x 19 Go board.[150]

362

[edit]

362 = 2 × 181. It is a zero of Mertens function,[106] a nontotient, a noncototient.[91]

362= σ2(19), the sum of squares of divisors of 19.[151]

363

[edit]

363=3 × 112. It is a deficient number, a perfect totient number,[152] a zero of Mertens function,[153] and a repdigit (BB) in base 32. It is a palindromic number in bases 3, 10, 11 and 32. It is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)[76] and the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).

363 can be expressed as the sum of three squares in four different ways:

363 = 112 + 112 + 112 = 52 + 72 + 172 = 12 + 12 + 192 = 132 + 132 + 52.

363 cubits is the solution given to Rhind Mathematical Papyrus question 50 – find the side length of an octagon with the same area as a circle 9 khet in diameter.

364

[edit]

364 = 22 × 7 × 13. It is a tetrahedral number,[154] a zero of Mertens function,[106] a nontotient, and the sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).[76]

It is a repdigit in base 3 (111111), base 9 (444), base 25 (EE), base 27 (DD), base 51 (77) and base 90 (44).

365

[edit]

366

[edit]

366 = 2 × 3 × 61. It is a sphenic number,[80] a zero of Mertens function,[106] a noncototient,[91] a 26-gonal number,[155] and a 123-gonal number.[156] There are 366 complete partitions of 20.[157]

There are 366 days in a leap year.[158]

367

[edit]

367 is a prime number,[76] a lucky prime,[103] a Perrin number,[159] a happy number in base 10, a prime index prime[160] and a strictly non-palindromic number.[161]

368

[edit]

368 = 24 × 23. It is a Leyland number.[77]

369

[edit]

369 = 32 × 41. 369 is the magic constant of the 9 × 9 magic square[162][163] and the n-Queens Problem for n = 9.[163] 369 forms a Ruth-Aaron Pair with 370 because the sums of their prime factors are equal.[164]

There are 369 free octominoes (polyominoes of order 8).[165][166]

370s

[edit]

370

[edit]

370 = 2 × 5 × 37. It is a sphenic number,[80] a nontotient, and a Base 10 Armstrong number since 33 + 73 + 03 = 370.[167] It forms a Ruth–Aaron pair with only distinct prime factors counted with 369.[168] It is the sum of four consecutive primes (83 + 89 + 97 + 101).[76]

371

[edit]

371 = 7 × 53. It is an Armstrong number since 33 + 73 + 13 = 371.[169] It is the sum of the primes from its least to its greatest prime factor, the next such composite number is 2935561623745.[170] It is the sum of three consecutive primes (113 + 127 + 131) and the sum of seven consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67).[76]

372

[edit]

372 = 22 × 3 × 31. It is a noncototient,[91] an untouchable number,[81] and a refactorable number.[95] It is the sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).[76]

373

[edit]

373 is a prime number,[76] a balanced prime,[171] a right and left-truncatable (two-sided prime),[172] a sexy prime with 367 and 379,[173] and a permutable prime with 337 and 733.[174] It is also a palindromic prime in 3 consecutive bases: 5658 = 4549 = 37310 and also in base 4: 113114. It is the sum of five consecutive primes (67 + 71 + 73 + 79 + 83).[76]

374

[edit]

374 = 2 × 11 × 17. It is a sphenic number[80] and a nontotient. 3744 + 1 is prime.[175]

375

[edit]

375 = 3 × 53. There are 375 regions in regular 11-gon with all diagonals drawn.[176]

376

[edit]

376 = 23 × 47. It is a pentagonal number,[99] a 1-automorphic number,[177] a nontotient, and a refactorable number.[95]

377

[edit]

377 is a semiprime and a deficient number.[178] 377 is the 7th centered octahedral number[179] and the 14th nonzero member of the Fibonacci sequence.[180]

378

[edit]

378 = 2 × 33 × 7. It is a cake number,[181] a hexagonal number,[182] and a Smith number.[74] It is the 27th triangular number.[183]

379

[edit]

379 is a prime number,[76] a Chen prime,[113] a lazy caterer number[92] and a happy number in base 10. It is the sum of the first 15 odd primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53). 379! - 1 is prime.

380s

[edit]

380

[edit]

380 = 22 × 5 × 19. It is a pronic number.[120] There are 380 regions when a figure made up of a row of 6 adjacent congruent rectangles is divided by drawing the diagonals of all possible rectangles.[184]

381

[edit]

381 = 3 × 127. It is palindromic in base 2 and base 8.

381 is the sum of the first 16 prime numbers (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).[185]

382

[edit]

382 = 2 × 191. It is a Smith number.[74] It is the sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).[76]

383

[edit]

383 is a prime number, a safe prime,[126] a Woodall prime,[186] a Thabit number,[187] an Eisenstein prime with no imaginary part, and a palindromic prime.[188] It is also the first number where the sum of a prime and the reversal of the prime is also a prime.[189] 4383 - 3383 is prime.[190]

384

[edit]

385

[edit]

385 = 5 × 7 × 11. It is a sphenic number[80] and a square pyramidal number.[191] There are 385 integer partitions of 18.[192]

385 = 102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12.

386

[edit]

386 = 2 × 193. It is a nontotient, a noncototient,[91] and a centered heptagonal number.[193] There are 388 surface points on a cube with edge-length 9.[194]

387

[edit]

387 = 32 × 43. There are 387 graphical partitions of 22.[195]

388

[edit]

388 = 22 × 97. It is the solution to the postage stamp problem with 6 stamps and 6 denominations.[196] There are 388 uniform rooted trees with 10 nodes.[197]

389

[edit]

389 is a prime number,[76] an emirp,[198] an Eisenstein prime with no imaginary part, a Chen prime,[113] a highly cototient number,[97] a strictly non-palindromic number.[199] It is the smallest conductor of a rank 2 Elliptic curve.

390s

[edit]

390

[edit]

390 = 2 × 3 × 5 × 13. It is a nontotient and the sum of four consecutive primes (89 + 97 + 101 + 103).[76]

is prime[200]

391

[edit]

391 = 17 × 23. It is a Smith number[74] and a centered pentagonal number.[104]

392

[edit]

392 = 23 × 72. It is an Achilles number.[201]

393

[edit]

393 = 3 × 131. It is a Blum integer[202] and a zero of Mertens function.[106]

394

[edit]

394 = 2 × 197 = S5 It is a Schröder number,[203] a nontotient, and a noncototient.[91]

395

[edit]

395 = 5 × 79. There are 395 (unordered, unlabeled) rooted trimmed trees with 11 nodes.[204]

395 is sum of three consecutive primes (127 + 131 + 137) and the sum of five consecutive primes (71 + 73 + 79 + 83 + 89).[76]

396

[edit]

396 = 22 × 32 × 11. It is the sum of twin primes (197 + 199), the totient sum of the first 36 integers,[205] a refactorable number,[95] a Harshad number, and a digit-reassembly number.

397

[edit]

397 is a prime number,[76] a cuban prime,[102] and a centered hexagonal number.[105]

398

[edit]

398 = 2 × 199. It is a nontotient.

is prime[200]

399

[edit]

399 = 3 × 7 × 19=. It is a sphenic number,[80] a Leyland number of the second kind,[206]and the smallest Lucas–Carmichael number.[207]

399! + 1 is prime.

399 is the largest number whose base 10 digit sum is larger than the square root of the number: 3 + 9 + 9 = 21, which is larger than 19.975.

References

[edit]
  1. ↑ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
  2. ↑ Sloane, N. J. A. (ed.). "Sequence A014105 (second hexagonal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "Sequence A008277". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "Sequence A007770 (Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ↑ Sloane, N. J. A. (ed.). "Sequence A007770 (Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ↑ Sloane, N. J. A. (ed.). "Sequence A005277". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ↑ Sloane, N. J. A. (ed.). "Sequence A000607 (Number of partitions of n into prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ↑ Sloane, N. J. A. (ed.). "Sequence A115981 (The number of compositions of n which cannot be viewed as stacks)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ↑ "Bipartite graphs". mathworld.wolfram.com.
  11. ↑ Salvatore, Jimmy. "Biparite Graphs and Problem Solving" (PDF). www.math.uchicago.edu.
  12. ↑ Sloane, N. J. A. (ed.). "Sequence A006036 (Primitive pseudoperfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ↑ Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers, also called non aliquot numbers: impossible values for the sum of aliquot parts function (A001065))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ↑ Sloane, N. J. A. (ed.). "Sequence A005277 (Nontotients: even numbers k such that phi(m) = k has no solution)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  15. ↑ Sloane, N. J. A. (ed.). "Sequence A067372 (Integers expressible as the sum of (at least two) consecutive primes in at least 2 ways)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ↑ Sloane, N. J. A. (ed.). "Sequence A005915". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. ↑ Sloane, N. J. A. (ed.). "Sequence A014342 (Convolution of primes with themselves)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ↑ "Pythagorean triples". mathworld.wolfram.com.
  19. ↑ Tobin-Campbell, Christopher. "Systems of Pythagorean Triples" (PDF). www.whitman.edu.
  20. ↑ Sloane, N. J. A. (ed.). "Sequence A002378". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ↑ Cooke, Robert (2013). The History of Mathematics (PDF). A John Wiley & Sons, Inc., Publication. p. 110. ISBN 9781118217566.
  22. ↑ Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function (A001065))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ↑ Pomerance, Carl; Yang, Hee-Sung. "On Untouchable Numbers and Related Probems" (PDF). math.dartmouth.edu.
  24. ↑ Bicknell, Marjorie; Hoggatt, V. E. "Triangular numbers" (PDF). mathstat.dal.ca.
  25. ↑ Sloane, N. J. A. (ed.). "Sequence A007510 (Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ↑ Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  27. ↑ Lewulis, Pawel (2016). "Chen primes in arithmetic progressions". arXiv:1601.02873 [math.NT].
  28. ↑ Sloane, N. J. A. (ed.). "Sequence A028818 (Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  29. ↑ Sloane, N. J. A. (ed.). "Sequence A006203 (Discriminants of imaginary quadratic fields with class number 3 (negated))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  30. ↑ Sloane, N. J. A. (ed.). "Sequence A006534 (Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  31. ↑ Sloane, N. J. A. (ed.). "Sequence A000293 (a(n) = number of solid (i.e., three-dimensional) partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ↑ Sloane, N. J. A. (ed.). "Sequence A005277 (Nontotients: even numbers k such that phi(m)=k has no solution)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. ↑ Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  34. ↑ Sloane, N. J. A. (ed.). "Sequence A001043 (Numbers that are the sum of 2 successive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ↑ Sloane, N. J. A. (ed.). "Sequence A046992 (a(n) = Sum_{k=1..n} pi(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  36. ↑ Sloane, N. J. A. (May 1, 2024). "The On-Line Encyclopedia of Integer Sequences". OEIS. Retrieved May 1, 2024.
  37. ↑ "sphenic number". mathworld.wolfram.com.
  38. ↑ "noncototient numbers". mathworld.wolfram.com.
  39. ↑ Sloane, N. J. A. (ed.). "Sequence A008930". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  40. ↑ Sloane, N. J. A. (ed.). "Sequence A006532 (Numbers whose sum of divisors is a square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  41. ↑ "Sloane's A000928 : Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  42. ↑ "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  43. ↑ "Tables of imaginary quadratic fields with small class number". numbertheory.org.
  44. ↑ Oakes, Mike (2001-02-23). "A059801 Numbers k such that 4^k - 3^k is prime". oeis.org. The On-Line Encyclopedia of Integer Sequences (OEIS). Retrieved February 18, 2026.
  45. ↑ "311edo". en.xen.wiki. Retrieved February 18, 2026.
  46. ↑ "A000926 - OEIS". oeis.org. Retrieved 2023-11-30.
  47. ↑ "A005349 - OEIS". oeis.org. Retrieved 2023-11-30.
  48. ↑ Sloane, N. J. A. (ed.). "Sequence A002144 (Pythagorean primes: primes of form 4*k + 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  49. ↑ "Sloane's A007703 : Regular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  50. ↑ Sloane, N. J. A. (ed.). "Sequence A020994 (Primes that are both left-truncatable and right-truncatable.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  51. ↑ Sloane, N. J. A. (ed.). "Sequence A001913 (Full reptend primes: primes with primitive root 10.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  52. ↑ Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  53. ↑ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  54. ↑ "Sloane's A007770 : Happy numbers]". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  55. ↑ Sloane, N. J. A. (ed.). "Sequence A005277". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  56. ↑ Sloane, N. J. A. (ed.). "Sequence A338908". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  57. ↑ Sloane, N. J. A. (ed.). "Sequence A011545". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  58. ↑ "A005448 - OEIS". oeis.org. Retrieved 2026-06-16.
  59. ↑ Sloane, N. J. A. (ed.). "Sequence A005448". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  60. ↑ Sloane, N. J. A. (ed.). "Sequence A069099". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  61. ↑ Sloane, N. J. A. (ed.). "Sequence A002858". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  62. ↑ Sloane, N. J. A. (ed.). "Sequence A001630". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  63. ↑ Sloane, N. J. A. (ed.). "Sequence A006749". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  64. ↑ Sloane, N. J. A. (ed.). "Sequence A053722". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  65. ↑ Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  66. ↑ Sloane, N. J. A. (ed.). "Sequence A020994 (Primes that are both left-truncatable and right-truncatable)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  67. ↑ "A003627 - OEIS". oeis.org. Retrieved 2026-06-16.
  68. ↑ "317 Day - 317 Day: Indianapolis celebrates its vibrant culture and creativity". wishtv.com. Retrieved 2026-07-06.
  69. ↑ Jackson, Cheryl V. "317 Day: March 17 events celebrate Indianapolis businesses, artists and culture". The Indianapolis Star. Retrieved 6 July 2026.
  70. ↑ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  71. ↑ "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  72. ↑ "A127339". oeis.org. Retrieved 2023-10-27.
  73. ↑ Sloane, N. J. A. (ed.). "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  74. 1 2 3 4 5 6 Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  75. ↑ Sloane, N. J. A. (ed.). "Sequence A007770 (Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  76. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Joyce, David E. "Prime numbers to 10000". Clark University. Retrieved 2026-06-30.
  77. 1 2 Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  78. ↑ "A003432 - OEIS". oeis.org. Retrieved 2026-06-16.
  79. ↑ Sloane, N. J. A. (ed.). "Sequence A001850 (Central Delannoy numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  80. 1 2 3 4 5 6 7 8 9 Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  81. 1 2 3 4 5 Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  82. ↑ Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  83. ↑ Sloane, N. J. A. (ed.). "Sequence A023759 (Nialpdromes: digits in base 3 are in nonincreasing order.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  84. ↑ Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function (A001065).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  85. ↑ Sloane, N. J. A. (ed.). "Sequence A002858 (Ulam numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  86. ↑ Sloane, N. J. A. (ed.). "Sequence A001694 (Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  87. ↑ Sloane, N. J. A. (ed.). "Sequence A002088 (Sum of totient function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  88. ↑ "What's Special About This Number?". erich-friedman.github.io. Retrieved 2026-07-19.
  89. ↑ Sloane, N. J. A. (ed.). "Sequence A034897 (Hyperperfect numbers: x such that x = 1 + k*(sigma(x)-x-1) for some k > 0)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  90. ↑ Sloane, N. J. A. (ed.). "Sequence A007594 (Smallest n-hyperperfect number: m such that m=n(sigma(m)-m-1)+1; or 0 if no such number exists)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  91. 1 2 3 4 5 6 7 8 9 Sloane, N. J. A. (ed.). "Sequence A005278 (Noncototients)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  92. 1 2 3 Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  93. ↑ Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  94. ↑ Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  95. 1 2 3 4 5 6 Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  96. ↑ "A007504 - OEIS". oeis.org. Retrieved 2026-06-16.
  97. 1 2 Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  98. ↑ "A000332 - OEIS". oeis.org. Retrieved 2026-06-16.
  99. 1 2 Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  100. ↑ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  101. ↑ "A006450 - OEIS". oeis.org. Retrieved 2026-06-16.
  102. 1 2 Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes: primes which are the difference of two consecutive cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  103. 1 2 Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  104. 1 2 Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  105. 1 2 Sloane, N. J. A. (ed.). "Sequence A003215 (Hex numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  106. 1 2 3 4 5 6 7 8 9 10 Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers n such that Mertens' function is zero)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  107. ↑ "A010785 - OEIS". oeis.org. Retrieved 2026-06-16.
  108. ↑ "A001037 - OEIS". oeis.org. Retrieved 2026-06-16.
  109. ↑ Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  110. ↑ Sloane, N. J. A. (ed.). "Sequence A000607 (Number of partitions of n into prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  111. ↑ "A006567 - OEIS". oeis.org. Retrieved 2026-06-16.
  112. ↑ "A003459 - OEIS". oeis.org. Retrieved 2026-06-16.
  113. 1 2 3 4 Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  114. ↑ Sloane, N. J. A. (ed.). "Sequence A122400 (Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  115. ↑ Sloane, N. J. A. (ed.). "Sequence A002858 (Ulam numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  116. ↑ "A000567 - OEIS". oeis.org. Retrieved 2026-07-02.
  117. ↑ "A005898 - OEIS". oeis.org. Retrieved 2026-07-02.
  118. ↑ Sloane, N. J. A. (ed.). "Sequence A050217 (Super-Poulet numbers: Poulet numbers whose divisors d all satisfy d|2^d-2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  119. ↑ Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  120. 1 2 Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  121. ↑ "A080035 - OEIS". oeis.org. Retrieved 2026-06-16.
  122. ↑ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  123. ↑ "A002088 - OEIS". oeis.org. Retrieved 2026-06-16.
  124. ↑ "A000926 - OEIS". oeis.org. Retrieved 2026-06-16.
  125. ↑ "A006567 - OEIS". oeis.org. Retrieved 2026-06-22.
  126. 1 2 Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  127. ↑ "A001359 - OEIS". oeis.org. Retrieved 2026-06-22.
  128. ↑ "A016038 - OEIS". oeis.org. Retrieved 2026-06-22.
  129. ↑ "A112419 - OEIS". oeis.org. Retrieved 2026-06-22.
  130. ↑ "A006512 - OEIS". oeis.org. Retrieved 2026-06-22.
  131. ↑ "A031157 - OEIS". oeis.org. Retrieved 2026-06-22.
  132. ↑ Sloane, N. J. A. (ed.). "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  133. ↑ Sloane, N. J. A. (ed.). "Sequence A006036 (Primitive pseudoperfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  134. ↑ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  135. ↑ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
  136. ↑ Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  137. ↑ "A000170 - OEIS". oeis.org. Retrieved 2026-06-22.
  138. ↑ Sloane, N. J. A. (ed.). "Sequence A000538 (Sum of fourth powers: 0^4 + 1^4 + ... + n^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  139. ↑ Sloane, N. J. A. (ed.). "Sequence A031971 (a(n) = Sum_{k=1..n} k^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  140. ↑ "A137275 - OEIS". oeis.org. Retrieved 2026-06-22.
  141. ↑ "A051953 - OEIS". oeis.org. Retrieved 2024-11-19.
  142. ↑ Sloane, N. J. A. (ed.). "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  143. ↑ "A003627 - OEIS". oeis.org. Retrieved 2026-06-16.
  144. ↑ "Chen prime". mathworld.wolfram.com.
  145. ↑ Sloane, N. J. A. (ed.). "Sequence A016038". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  146. ↑ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  147. ↑ "A016754 - OEIS". oeis.org. Retrieved 2026-06-23.
  148. ↑ Sloane, N. J. A. (ed.). "Sequence A062786 (Centered 10-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  149. ↑ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  150. ↑ "Go | History & Rules | Britannica". Encyclopedia Britannica. Retrieved 2026-06-23.
  151. ↑ Sloane, N. J. A. (ed.). "Sequence A001157 (a(n) = sigma_2(n): sum of squares of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  152. ↑ "A082897 - OEIS". oeis.org. Retrieved 2026-07-01.
  153. ↑ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  154. ↑ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers (or triangular pyramidal))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  155. ↑ "A316724 - OEIS". oeis.org. Retrieved 2026-06-23.
  156. ↑ "Polygonal Numbers". www.virtuescience.com. Retrieved 2026-06-23.
  157. ↑ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  158. ↑ "What Is a Leap Year? | NASA Space Place – NASA Science for Kids". spaceplace.nasa.gov. Retrieved 2026-06-23.
  159. ↑ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  160. ↑ "A006450 - OEIS". oeis.org. Retrieved 2026-06-23.
  161. ↑ "A016038 - OEIS". oeis.org. Retrieved 2026-06-22.
  162. ↑ Kraitchik, M (1942). "Magic Squares". Mathematical Recreations. New York: Norton. pp. 142–192.
  163. 1 2 Sequence A006003 in OEIS.
  164. ↑ "Ruth-Aaron Pair". mathworld.wolfram.com.
  165. ↑ Redelmeier, D. Hugh (1981). "Counting polyominoes: yet another attack". Discrete Mathematics. 36 (2): 191–203. doi:10.1016/0012-365X(81)90237-5.
  166. ↑ Sequence A000105 in OEIS.
  167. ↑ "A005188 - OEIS". oeis.org. Retrieved 2026-06-23.
  168. ↑ "A006145 - OEIS". oeis.org. Retrieved 2026-06-23.
  169. ↑ "A005188 - OEIS". oeis.org. Retrieved 2026-06-23.
  170. ↑ Sloane, N. J. A. (ed.). "Sequence A055233 (Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  171. ↑ Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  172. ↑ Sloane, N. J. A. (ed.). "Sequence A020994 (Primes that are both left-truncatable and right-truncatable)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  173. ↑ "A046119 - OEIS". oeis.org. Retrieved 2026-06-23.
  174. ↑ "A003459 - OEIS". oeis.org. Retrieved 2026-06-23.
  175. ↑ Sloane, N. J. A. (ed.). "Sequence A000068 (Numbers k such that k^4 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  176. ↑ Sloane, N. J. A. (ed.). "Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  177. ↑ Sloane, N. J. A. (ed.). "Sequence A003226 (Automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  178. ↑ "Number 377 - Facts about the integer". Numbermatics - the number explorer. Retrieved 9 August 2025.
  179. ↑ Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  180. ↑ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  181. ↑ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
  182. ↑ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  183. ↑ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
  184. ↑ Sloane, N. J. A. (ed.). "Sequence A306302 (Number of regions into which a figure made up of a row of n adjacent congruent rectangles is divided upon drawing diagonals of all possible rectangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  185. ↑ "A007504 - OEIS". oeis.org. Retrieved 2026-06-23.
  186. ↑ Sloane, N. J. A. (ed.). "Sequence A050918 (Woodall primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  187. ↑ "A055010 - OEIS". oeis.org. Retrieved 2026-06-23.
  188. ↑ "A002385 - OEIS". oeis.org. Retrieved 2026-06-23.
  189. ↑ Sloane, N. J. A. (ed.). "Sequence A072385 (Primes which can be represented as the sum of a prime and its reverse)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  190. ↑ "A059801 - OEIS". oeis.org. Retrieved 2026-06-23.
  191. ↑ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  192. ↑ "A000041 - OEIS". oeis.org. Retrieved 2026-06-23.
  193. ↑ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  194. ↑ Sloane, N. J. A. (ed.). "Sequence A005897 (a(n) = 6*n^2 + 2 for n > 0, a(0)=1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  195. ↑ Sloane, N. J. A. (ed.). "Sequence A000569 (Number of graphical partitions of 2n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  196. ↑ Sloane, N. J. A. (ed.). "Sequence A084192 (Array read by antidiagonals: T(n,k) = solution to postage stamp problem with n stamps and k denominations (n >= 1, k >= 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  197. ↑ Sloane, N. J. A. (ed.). "Sequence A317712 (Number of uniform rooted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  198. ↑ "A006567 - OEIS". oeis.org. Retrieved 2026-06-22.
  199. ↑ "A016038 - OEIS". oeis.org. Retrieved 2026-06-22.
  200. 1 2 Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  201. ↑ "A052486 - OEIS". oeis.org. Retrieved 2026-06-23.
  202. ↑ "A016105 - OEIS". oeis.org. Retrieved 2026-07-02.
  203. ↑ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  204. ↑ Sloane, N. J. A. (ed.). "Sequence A002955 (Number of (unordered, unlabeled) rooted trimmed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  205. ↑ "A002088 - OEIS". oeis.org. Retrieved 2026-07-02.
  206. ↑ Sloane, N. J. A. (ed.). "Sequence A045575 (Leyland numbers of the second kind)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  207. ↑ "A006972 - OEIS". oeis.org. Retrieved 2026-06-23.
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