A023821 Sum of exponents in prime-power factorization of C(3n,n-2).

0, 2, 3, 3, 6, 5, 6, 8, 8, 9, 11, 9, 10, 10, 12, 11, 12, 13, 13, 14, 17, 15, 17, 17, 16, 18, 19, 17, 20, 17, 19, 21, 19, 19, 22, 20, 20, 21, 22, 21, 23, 26, 26, 28, 29, 25, 29, 28, 27, 28, 29, 26, 32, 31, 31, 32, 30, 31, 33, 33, 31, 31, 35, 33, 32, 30, 31, 32, 36, 32, 35, 34, 33, 38, 37, 35, 38, 35

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A001222, A003408, A023819, A023820, A023822, A023823, A023824, A023825..

Programs

Mathematica

Join[{0},Table[Total[Transpose[FactorInteger[Binomial[3n,n-2]]][[2]]],{n,3,80}]] (* Harvey P. Dale, Sep 23 2014 *)
a[n_] := PrimeOmega[Binomial[3*n, n-2]]; Array[a, 100, 2] (* Amiram Eldar, Jun 12 2025 *)

PARI

a(n) = bigomega(binomial(3*n, n-2)); \\ Amiram Eldar, Jun 12 2025

Formula

From Amiram Eldar, Jun 12 2025: (Start)

a(n) = A001222(A003408(n-2)).

a(n) = A023820(n) - A001222(2*n+2) + A001222(n-1). (End)