cp's OEIS Frontend

A201733 Number of isomorphism classes of polycyclic groups (or solvable groups) of order n.

%I A201733 #27 Nov 03 2017 03:43:35
%S A201733 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,
%T A201733 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,
%U A201733 267,1,4,1,5,1,4,1,50,1,2,3,4,1,6,1,52,15,2,1
%N A201733 Number of isomorphism classes of polycyclic groups (or solvable groups) of order n.
%C A201733 For finite groups solvable is equivalent to polycyclic.
%H A201733 Muniru A Asiru, <a href="/A201733/b201733.txt">Table of n, a(n) for n = 1..500</a>
%H A201733 Wikipedia, <a href="http://en.wikipedia.org/wiki/Polycyclic_group">Polycyclic group</a>
%H A201733 Wikipedia, <a href="http://en.wikipedia.org/wiki/Solvable_groups">Solvable group</a>
%F A201733 a(n) = A000001(n) for n < 60.
%F A201733 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
%o A201733 (GAP)
%o A201733 a:=[];;
%o A201733 N:=120;;
%o A201733 for n in [1..N] do
%o A201733 a[n]:=0;;
%o A201733 for j in [1..NrSmallGroups(n)] do
%o A201733    if IsPcGroup(SmallGroup(n,j)) = true then
%o A201733     a[n]:=a[n]+1;
%o A201733    fi;
%o A201733   od;
%o A201733   Print(a[n],",");
%o A201733 od;
%K A201733 nonn
%O A201733 1,4
%A A201733 _W. Edwin Clark_, Dec 04 2011