A023984 Sum of exponents in prime-power factorization of multinomial coefficient M(6n; n,n,n,n,n,n).

0, 7, 13, 20, 21, 29, 33, 40, 37, 40, 43, 54, 51, 59, 64, 67, 60, 69, 67, 76, 75, 79, 85, 95, 88, 91, 96, 96, 93, 102, 102, 111, 101, 104, 108, 114, 106, 115, 121, 125, 118, 130, 130, 143, 142, 140, 146, 155, 144, 147, 148, 153, 151, 159, 157, 162, 155, 159, 164, 177, 170, 180, 186

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A008979, A022559.

Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023985, A023986, A023987, A023990, A023991, A023992, A023993.

Programs

Mathematica

a[n_] := PrimeOmega[Multinomial[n, n, n, n, n, n]]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2025 *)

PARI

a(n) = bigomega((6*n)! / (n!)^6); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A008979(n)).

a(n) = A022559(6*n) - 6*A022559(n). (End)

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 11 2025