A048570 - OEIS

%I #16 Apr 08 2022 08:16:43

%S 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,

%T 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,

%U 4,1,1,2,4,8,16,16,16,16,8,4,2,1,1,6,8,12,12,24,24,24

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

%H T. D. Noe, <a href="/A048570/b048570.txt">Rows n = 0..100 of triangle, flattened</a>

%F T(n, k) = A000005(A007318(n, k)). - _Michel Marcus_, Mar 07 2020

%e Triangle begins

%e   1;

%e   1, 1;

%e   1, 2, 1;

%e   1, 2, 2, 1;

%e   1, 3, 4, 3, 1;

%e   1, 2, 4, 4, 2, 1;

%e   1, 4, 4, 6, 4, 4, 1;

%e   ...

%t Flatten[Table[DivisorSigma[0,Binomial[n,k]],{n,0,12},{k,0,n}]] (* _Stefano Spezia_, Apr 07 2022 *)

%o (PARI) T(n, k) = if (n>=k, numdiv(binomial(n, k))); \\ _Michel Marcus_, Mar 07 2020

%Y Cf. A000005, A007318.

%K nonn,tabl,easy

%O 0,5

%A _N. J. A. Sloane_