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A201733 Number of isomorphism classes of polycyclic groups (or solvable groups) of order n. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A318475 A066083 A128644 * A000001 A172133 A146002

Adjacent sequences: A201730 A201731 A201732 * A201734 A201735 A201736

KEYWORD

nonn

AUTHOR

W. Edwin Clark, Dec 04 2011

STATUS

approved

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Last modified December 2 15:00 EST 2022. Contains 358510 sequences. (Running on oeis4.)