A020738 Consider number of divisors of binomial(n, k), k=0..n; a(n) = multiplicity of the maximum value.

2, 1, 2, 1, 2, 1, 4, 3, 4, 1, 4, 3, 2, 1, 2, 1, 6, 2, 6, 2, 6, 1, 8, 2, 2, 1, 4, 2, 2, 1, 10, 4, 2, 5, 2, 2, 2, 1, 2, 1, 6, 2, 2, 2, 4, 1, 2, 1, 2, 2, 6, 2, 4, 2, 2, 4, 2, 1, 10, 2, 2, 3, 4, 8, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 6, 2, 2, 2, 12, 2, 2, 1, 2, 4, 4, 2, 2, 2, 2, 1, 2, 2, 2, 1, 4, 2, 4, 2

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			If n = 23, the numbers of divisors of {binomial(23, k)} are {1, 2, 4, 8, 16, 16, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 32, ...}. The maximum occurs 8 times, so a(23) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert Israel)

Crossrefs

Cf. A000005, A048485, A048569, A048570.

Programs

Maple

f:= proc(n) local L,k;
  L:= [seq(numtheory:-tau(binomial(n,k)),k=0..n)];
  numboccur(max(L),L)
end proc:
map(f, [$1..200]); # Robert Israel, Nov 17 2016

Mathematica

a[ n_] := If[ n < 1, 0, Last @ Last @ Tally @ Array[ Length @ Divisors @ Binomial[n, #] &, n+1, 0]]; (* Michael Somos, Nov 17 2016 *)