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%I #31 Jun 26 2022 10:23:41
%S 0,1,1,2,1,2,1,3,2,2,1,2,1,2,1,4,1,3,1,2,2,2,1,3,2,2,3,2,1,2,1,5,1,2,
%T 1,3,1,2,2,3,1,2,1,2,2,2,1,4,2,3,1,2,1,4,2,3,2,2,1,2,1,2,2,6,1,2,1,2,
%U 1,2,1,3,1,2,2
%N Maximal size of a minimal-generating-set of G where G is a finite group of order n.
%C a(n) <= floor(log_2(n)) with equality if n=2^m is a power of 2.
%C For n >= 2, a(n) = 1 iff n belongs to sequence A003277.
%C a(n) >= A051903(n). - _Álvar Ibeas_, Mar 28 2015
%C a(p^2) = 2 for all primes p, since there are only two groups (up to isomorphism) of order p^2: Z_p^2 and Z_p X Z_p. The latter is generated by 2 elements. - _Tom Edgar_, Apr 06 2015
%H Jinyuan Wang, <a href="/A059829/b059829.txt">Table of n, a(n) for n = 1..511</a> (terms 1..150 from Robert Israel)
%e Up to isomorphism, there are five groups of order 8: the two non-abelian groups (the dihedral group and the quaternion group) are both generated by two elements, and the three abelian groups are Z_8 (generated by 1 element), Z_2 X Z_4 (generated by 2 elements) and Z_2 X Z_2 X Z_2 (generated by 3 elements). Thus a(8) = 3.
%o (GAP)
%o A := [0];
%o for n in [2 .. 100] do
%o G := AllSmallGroups(n);
%o m := NumberSmallGroups(n);
%o t := 1;
%o for i in [ 1 .. m] do
%o while EulerianFunction(G[i],t) = 0 do
%o t:= t+1;
%o od;
%o od;
%o A[n]:= t;
%o od;
%o A;# _Robert Israel_, Apr 01 2015
%Y Cf. A003277, A051903.
%K nonn
%O 1,4
%A Noam Katz (noamkj(AT)hotmail.com), Feb 25 2001
%E Offset and first term corrected by _Álvar Ibeas_, Mar 27 2015
%E More terms from _Robert Israel_, Apr 01 2015
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