A048570 Triangle T(n,k) = number of divisors of binomial(n,k).

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 2, 4, 4, 2, 1, 1, 4, 4, 6, 4, 4, 1, 1, 2, 4, 4, 4, 4, 2, 1, 1, 4, 6, 8, 8, 8, 6, 4, 1, 1, 3, 9, 12, 12, 12, 12, 9, 3, 1, 1, 4, 6, 16, 16, 18, 16, 16, 6, 4, 1, 1, 2, 4, 8, 16, 16, 16, 16, 8, 4, 2, 1, 1, 6, 8, 12, 12, 24, 24, 24

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins
  1;
  1, 1;
  1, 2, 1;
  1, 2, 2, 1;
  1, 3, 4, 3, 1;
  1, 2, 4, 4, 2, 1;
  1, 4, 4, 6, 4, 4, 1;
  ...
		

Links

• T. D. Noe, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A000005, A007318.

Programs

Mathematica

Flatten[Table[DivisorSigma[0,Binomial[n,k]],{n,0,12},{k,0,n}]] (* Stefano Spezia, Apr 07 2022 *)

PARI

T(n, k) = if (n>=k, numdiv(binomial(n, k))); \\ Michel Marcus, Mar 07 2020

Formula

T(n, k) = A000005(A007318(n, k)). - Michel Marcus, Mar 07 2020