A066389 - OEIS

A066389

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>.

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

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OFFSET

1,4

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1023

PROG

(GAP)

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

CROSSREFS

Cf. A000001.

Sequence in context: A345344 A319004 A234541 * A077191 A317545 A319002

Adjacent sequences: A066386 A066387 A066388 * A066390 A066391 A066392

KEYWORD

nonn,nice

AUTHOR

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

EXTENSIONS

More terms from Reiner Martin, Dec 29 2001

More terms from Eric M. Schmidt, May 02 2013

STATUS

approved