A023822 Sum of exponents in prime-power factorization of C(3n,n-3).

0, 3, 3, 6, 5, 7, 7, 10, 9, 10, 9, 12, 9, 12, 12, 14, 13, 15, 12, 19, 15, 17, 17, 18, 18, 20, 19, 20, 16, 21, 20, 23, 20, 21, 20, 23, 18, 23, 21, 25, 26, 27, 27, 30, 27, 28, 28, 31, 27, 31, 27, 33, 31, 33, 31, 32, 31, 33, 31, 34, 30, 36, 34, 34, 31, 33, 31, 37, 32, 35, 34, 37, 36, 37, 37, 39, 35, 37

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A001222, A004321, A023819, A023820, A023822, A023823, A023824, A023825.

Programs

Mathematica

Join[{0}, Table[Total[FactorInteger[Binomial[3 n, n - 3]][[All, 2]]], {n, 4, 80}]] (* Ivan Neretin, Nov 02 2017 *)
a[n_] := PrimeOmega[Binomial[3*n, n-3]]; Array[a, 100, 3] (* Amiram Eldar, Jun 12 2025 *)

PARI

a(n) = bigomega(binomial(3*n, n-3)); \\ Amiram Eldar, Jun 12 2025

Formula

From Amiram Eldar, Jun 12 2025: (Start)

a(n) = A001222(A004321(n)).

a(n) = A023821(n) - A001222(2*n+3) + A001222(n-2). (End)

Extensions

Offset corrected to 3 by Ivan Neretin, Nov 02 2017