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