A102445 Number of prime divisors (counted with multiplicity) of the central trinomial coefficients (A002426).

0, 1, 1, 1, 2, 2, 2, 4, 2, 2, 3, 2, 2, 4, 3, 4, 6, 3, 2, 3, 3, 5, 6, 6, 4, 9, 3, 3, 2, 3, 3, 4, 5, 3, 5, 4, 2, 3, 3, 4, 2, 7, 5, 7, 7, 5, 5, 6, 6, 4, 5, 8, 9, 4, 5, 6, 3, 3, 7, 6, 8, 7, 7, 4, 5, 4, 4, 7, 7, 9, 11, 5, 8, 7, 7, 6, 7, 7, 8, 12, 4, 7, 6, 6, 4, 8, 7, 4, 10, 7, 7, 6, 6, 7, 5, 5, 6, 8, 7, 9, 10, 5, 7

Offset: 1

Author

Jonathan Vos Post, Feb 21 2005

Keywords

• nonn

Comments

First occurrence of k: 1,2,5,11,8,22,17,42,52,26,89,71,80,....

Links

• Amiram Eldar, Table of n, a(n) for n = 1..218
• Eric Weisstein's World of Mathematics, Trinomial Coefficient..

Crossrefs

Cf. A001222, A002426.

Programs

Mathematica

bigomega[n_Integer] := Plus @@ Last /@ FactorInteger[n]; tn[n_] := Sum[Binomial[n, k]*Binomial[n - k, k], {k, 0, n/2}]; Table[bigomega[tn[n]], {n, 103}] (* Robert G. Wilson v, Feb 21 2005 *)

Formula

a(n) = A001222(A002426(n)). - Amiram Eldar, Feb 06 2020

Extensions

Edited and extended by Robert G. Wilson v, Feb 21 2005