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

0,12

Links

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

Formula

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

Example

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;

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

Crossrefs

Cf. A048571, which counts only distinct factors.

Cf. A001222, A007318.

Sequence in context: A123186 A127323 A327298 * A089789 A257921 A261119

Adjacent sequences: A132893 A132894 A132895 * A132897 A132898 A132899

Keyword

nonn,tabl

Author

Emeric Deutsch, Oct 16 2007

Status

approved