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

0,5

Links

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

Formula

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

Example

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;
  ...

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A007318.

Sequence in context: A156044 A180980 A275298 * A090806 A241926 A174446

Adjacent sequences: A048567 A048568 A048569 * A048571 A048572 A048573

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane

Status

approved