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

0,13

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.

Formula

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

Example

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
...

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 *)

Crossrefs

Cf. A048273, A132896.

Cf. A001221, A007318.

Sequence in context: A342955 A004197 A261684 * A025880 A058755 A128519

Adjacent sequences: A048568 A048569 A048570 * A048572 A048573 A048574

Keyword

nonn,tabl

Author

N. J. A. Sloane; edited Oct 06 2007 at the suggestion of T. D. Noe.

Extensions

Corrected by T. D. Noe, Oct 19 2007

Status

approved