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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

If n=23, the divisors for {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.

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 *)

Crossrefs

Cf. A000005, A048485, A048569, A048570.

Sequence in context: A029218 A100376 A336318 * A063279 A247051 A247050

Adjacent sequences: A020735 A020736 A020737 * A020739 A020740 A020741

Keyword

nonn

Author

Labos Elemer

Status

approved