A066389 - OEIS

%I #11 Oct 30 2022 18:19:59

%S 1,1,1,2,1,2,1,4,2,2,1,5,1,2,1,9,1,4,1,5,2,2,1,13,2,2,4,4,1,4,1,20,1,

%T 2,1,12,1,2,2,12,1,6,1,4,2,2,1,35,2,4,1,5,1,10,2,11,2,2,1,13,1,2,4,54,

%U 1,4,1,5,1,4,1,37,1,2,3,4,1,6,1,35,10,2,1

%N Number of 2-generated groups of order n: groups that have a generating set of size <=2, i.e., are cyclic or of the form <a,b>.

%H Eric M. Schmidt, <a href="/A066389/b066389.txt">Table of n, a(n) for n = 1..1023</a>

%o (GAP)

%o IsTwoGenerated := function(G) if IsSolvableGroup(G) then return (Length(MinimalGeneratingSet(G)) <= 2); fi; return ForAny(List(ConjugacyClasses(G), Representative), g->ForAny(G, h->Size(Group(g, h)) = Size(G))); end; A066389 := function(n) local count, i; count := 0; for i in [1..NumberSmallGroups(n)] do if IsTwoGenerated(SmallGroup(n, i)) then count := count + 1; fi; od; return count; end; # _Eric M. Schmidt_, May 02 2013; shortened by _Eric M. Schmidt_, May 20 2013

%Y Cf. A000001.

%K nonn,nice

%O 1,4

%A Sharon Sela (sharonsela(AT)hotmail.com), Dec 23 2001

%E More terms from _Reiner Martin_, Dec 29 2001

%E More terms from _Eric M. Schmidt_, May 02 2013