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 A241276 Number of partitions of n that come from sizes of conjugacy classes of groups of order n. 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS a(n) = 1 if every group of order n is abelian, that is, if n is in A051532. Upper bounds are given by A000001 (number of groups of order n) and A018818 (number of partitions of n into divisors of n). A077191 is an upper bound. - Eric M. Schmidt, Oct 16 2014 LINKS Eric M. Schmidt, Table of n, a(n) for n = 1..1023 Wikipedia, Conjugacy Class EXAMPLE 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. PROG (GAP) a:=[];; for n in [1..100] do   P:=[];   for i in [1..NumberSmallGroups(n)] do    g:=SmallGroup(n, i);    cc:=ConjugacyClasses(g);    L:=List(cc, Size);    Sort(L);    Add(P, L);    P:=Set(P);   od;   Add(a, Length(P)); od; a; (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 CROSSREFS Sequence in context: A087942 A327925 A320012 * A325759 A292286 A099042 Adjacent sequences:  A241273 A241274 A241275 * A241277 A241278 A241279 KEYWORD nonn,hard AUTHOR W. Edwin Clark, Apr 18 2014 STATUS approved

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Last modified June 2 16:27 EDT 2020. Contains 334787 sequences. (Running on oeis4.)