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A048475
a(n) is the smallest k at which the number of divisors of binomial(n,k) is maximized.
2
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
1,4
LINKS
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved