A048475 a(n) is the smallest k at which the number of divisors of binomial(n,k) is maximized.

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, 11, 13, 13, 14, 15, 17, 18, 19, 19, 20, 18, 19, 20, 21, 19, 23, 23, 24, 23, 24, 20, 23, 22, 23, 24, 23, 28, 29, 21, 29, 23, 23, 29, 21, 31, 29, 29, 24, 31, 29, 24, 29, 29, 31, 31, 33

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A000005, A048275, A001405, A048570.

Programs

Mathematica

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 *)