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%I #15 May 28 2018 09:13:26
%S 0,1,1,2,2,3,2,3,3,5,4,5,6,7,7,8,6,7,6,7,7,11,8,11,11,13,12,13,14,15,
%T 11,13,13,14,15,17,18,19,19,20,18,19,20,21,19,23,23,24,23,24,20,23,22,
%U 23,24,23,28,29,21,29,23,23,29,21,31,29,29,24,31,29,24,29,29,31,31,33
%N a(n) is the smallest k at which the number of divisors of binomial(n,k) is maximized.
%H Giovanni Resta, <a href="/A048475/b048475.txt">Table of n, a(n) for n = 1..4000</a>
%e For n=50, the number of divisors of {C(50,k)} is maximal if k=24,26: A000005(C(50,24)) = A000005(C(50,26)) = 5184. The number of divisors of the central (median) value, A000005(C(50,25)) = 4608, is smaller.
%t a[n_] := Block[{d = DivisorSigma[0, Binomial[n, Range[0, n/2]]]}, Position[ d, Max[d], 1, 1][[1, 1]] - 1]; Array[a, 76] (* _Giovanni Resta_, May 14 2018 *)
%Y Cf. A000005, A048275, A001405, A048570.
%K nonn
%O 1,4
%A _Labos Elemer_