A023978 Sum of exponents in prime-power factorization of multinomial coefficient M(3n; n,n,n).

0, 2, 4, 7, 7, 9, 11, 14, 12, 13, 14, 19, 18, 20, 22, 23, 19, 23, 22, 27, 25, 25, 30, 33, 30, 30, 32, 33, 31, 34, 34, 38, 33, 34, 36, 38, 34, 37, 40, 42, 39, 42, 43, 50, 49, 48, 50, 54, 49, 50, 49, 51, 51, 53, 54, 55, 51, 53, 54, 61, 57, 60, 63, 63, 56, 56, 56, 61, 60, 61, 63, 66, 61, 64, 67, 69, 67, 68

Offset

0,2

Links

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

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A006480(n)).

a(n) = A022559(3*n) - 3*A022559(n). (End)

Mathematica

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

Prog

(PARI) a(n) = bigomega((3*n)! / n!^3); \\ Amiram Eldar, Jun 11 2025

Crossrefs

Cf. A001222, A006480, A022559.

Cf. A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.

Sequence in context: A393402 A161368 A396009 * A152488 A109359 A025087

Adjacent sequences: A023975 A023976 A023977 * A023979 A023980 A023981

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved