A048571 Triangle read by rows: T(n,k) = number of distinct prime factors of C(n,k).

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 3, 2, 2, 1, 0, 0, 1, 2, 3, 3, 3, 3, 2, 1, 0, 0, 2, 2, 3, 4, 3, 4, 3, 2, 2, 0, 0, 1, 2, 3, 4, 4, 4, 4, 3, 2, 1, 0, 0, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3, 2, 0

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• tabl

Examples

			Triangle begins:
0
0,0
0,1,0
0,1,1,0
0,1,2,1,0
0,1,2,2,1,0
0,2,2,2,2,2,0
0,1,2,2,2,2,1,0
...
		

Links

• T. D. Noe, Rows n=0..100 of triangle, flattened
• Pierre Goetgheluck, On prime divisors of binomial coefficients, Math. Comp. 51 (1988), no. 183, 325-329.

Crossrefs

Cf. A048273, A132896.

Cf. A001221, A007318.

Programs

Mathematica

Flatten[Table[b=Binomial[n,k]; If[b==1, 0, Length[FactorInteger[b]]], {n,0,12}, {k,0,n}]] (* T. D. Noe, Oct 19 2007, Apr 03 2012 *)
Table[PrimeNu[Binomial[n,k]],{n,0,15},{k,0,n}]//Flatten (* Harvey P. Dale, Jun 11 2019 *)

Formula

T(n, k) = A001221(A007318(n, k)). - Michel Marcus, Nov 04 2020

Extensions

Edited Oct 06 2007 at the suggestion of T. D. Noe

Corrected by T. D. Noe, Oct 19 2007