A132896 Triangle read by rows: T(n,k)=number of prime divisors of C(n,k), counted with multiplicity (0<=k<=n).

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 3, 2, 2, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 3, 3, 4, 3, 4, 3, 3, 0, 0, 2, 4, 4, 4, 4, 4, 4, 2, 0, 0, 2, 3, 5, 4, 5, 4, 5, 3, 2, 0, 0, 1, 2, 3, 4, 4, 4, 4, 3, 2, 1, 0, 0, 3, 3, 4, 4, 6, 5, 6, 4, 4, 3, 3, 0

Offset: 0

Author

Emeric Deutsch, Oct 16 2007

Keywords

• nonn
• tabl

Examples

			T(8,3)=4 because C(8,3)=56=2*2*2*7.
Triangle begins:
0;
0,0;
0,1,0;
0,1,1,0;
0,2,2,2,0;
0,1,2,2,1,0;
		

Links

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

Crossrefs

Cf. A048571, which counts only distinct factors.

Cf. A001222, A007318.

Programs

Maple

with(numtheory): T:=proc(n,k) if k <= n then bigomega(binomial(n,k)) else x end if end proc: for n from 0 to 12 do seq(T(n,k),k=0..n) end do; # yields sequence in triangular form

Formula

T(n, k) = A001222(A007318(n, k)). - Michel Marcus, Nov 04 2020