# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a241276 Showing 1-1 of 1 %I A241276 #21 Dec 13 2018 09:09:45 %S A241276 1,1,1,1,1,2,1,2,1,2,1,3,1,2,1,3,1,3,1,3,2,2,1,7,1,2,2,2,1,4,1,6,1,2, %T A241276 1,6,1,2,2,5,1,6,1,2,1,2,1,13,1,3,1,3,1,7,2,5,2,2,1,9,1,2,2,16,1,4,1, %U A241276 3,1,4,1,17,1,2,2,2,1,6,1,11,3,2,1,9,1,2,1,4,1,6,1,2,2,2,1,30,1,3,1,7 %N A241276 Number of partitions of n that come from sizes of conjugacy classes of groups of order n. %C A241276 a(n) = 1 if every group of order n is abelian, that is, if n is in A051532. %C A241276 Upper bounds are given by A000001 (number of groups of order n) and A018818 (number of partitions of n into divisors of n). %C A241276 A077191 is an upper bound. - _Eric M. Schmidt_, Oct 16 2014 %H A241276 Eric M. Schmidt, Table of n, a(n) for n = 1..1023 %H A241276 Wikipedia, Conjugacy Class %e A241276 If n = 6 there are two groups of order 6: Z_6, all of whose conjugacy classes are of order 1 giving the partition [1,1,1,1,1,1] and S_6, which has three conjugacy classes whose sizes are 1, 2 and 3, giving the partition [1,2,3]. Hence a(6) = 2. %o A241276 (GAP) %o A241276 a:=[];; %o A241276 for n in [1..100] do %o A241276 P:=[]; %o A241276 for i in [1..NumberSmallGroups(n)] do %o A241276 g:=SmallGroup(n,i); %o A241276 cc:=ConjugacyClasses(g); %o A241276 L:=List(cc,Size); %o A241276 Sort(L); %o A241276 Add(P,L); %o A241276 P:=Set(P); %o A241276 od; %o A241276 Add(a,Length(P)); %o A241276 od; %o A241276 a; %o A241276 (GAP) a := function(n) local i, p, P; P := []; for i in [1..NrSmallGroups(n)] do p := List(ConjugacyClasses(SmallGroup(n,i)), Size); Sort(p); MakeImmutable(p); AddSet(P, p); od; return Length(P); end; # _Eric M. Schmidt_, Oct 16 2014 %K A241276 nonn,hard %O A241276 1,6 %A A241276 _W. Edwin Clark_, Apr 18 2014 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE