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%I #22 Oct 07 2019 03:05:42
%S 1,2,4,4,8,2,4,8,8,2,4,8,16,16,16,16,32,16,32,16,64,64,128,32,32,32,
%T 64,32,64,32,64,128,512,128,128,128,256,256,256,256,512,1024,2048,
%U 1024,512,128,256,128,128,256,1024,512,1024,256,1024,4096,16384,4096,8192
%N Multiplicity of Max{gcd(d, n!/d)} when d runs over the divisors of n!.
%C All terms are powers of 2.
%F It appears that a(n) = 2^A055460(n). - _Joerg Arndt_, Oct 06 2019
%e n=5, 5!=120, the set of gcd(d, 120/d) values for the 16 divisors of 120 is {1,2,1,2,1,2,1,2,2,1,2,1,2,1,2,1}. The maximum is 2 and it occurs 8 times, so a(5)=8.
%t Table[Count[#, Max@ #] &@ Map[GCD[#, m/#] &, Divisors[m]], {m, Range[30]!}] (* _Michael De Vlieger_, Oct 06 2019 *)
%Y Cf. A000188.
%K nonn
%O 1,2
%A _Labos Elemer_, Jun 13 2000
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