A201733 - OEIS

A201733

Number of isomorphism classes of polycyclic groups (or solvable groups) of order n.

1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, 2, 1, 14, 1, 5, 1, 5, 2, 2, 1, 15, 2, 2, 5, 4, 1, 4, 1, 51, 1, 2, 1, 14, 1, 2, 2, 14, 1, 6, 1, 4, 2, 2, 1, 52, 2, 5, 1, 5, 1, 15, 2, 13, 2, 2, 1, 12, 1, 2, 4, 267, 1, 4, 1, 5, 1, 4, 1, 50, 1, 2, 3, 4, 1, 6, 1, 52, 15, 2, 1

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OFFSET

1,4

COMMENTS

For finite groups solvable is equivalent to polycyclic.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..500

Wikipedia, Polycyclic group

Wikipedia, Solvable group

FORMULA

a(n) = A000001(n) for n < 60.

a(n) <= A000001(n) with equality if and only if n is not in A056866. In particular a(n) = A000001(n) for odd n (this is the Feit-Thompson theorem). - Benoit Jubin, Mar 30 2012

PROG

(GAP)

a:=[];;

N:=120;;

for n in [1..N] do

a[n]:=0;;

for j in [1..NrSmallGroups(n)] do

if IsPcGroup(SmallGroup(n, j)) = true then

a[n]:=a[n]+1;

fi;

od;

Print(a[n], ", ");

od;

CROSSREFS

Sequence in context: A066083 A128644 A396721 * A000001 A172133 A146002

Adjacent sequences: A201730 A201731 A201732 * A201734 A201735 A201736

KEYWORD

nonn

AUTHOR

W. Edwin Clark, Dec 04 2011

STATUS

approved