A023819 Sum of exponents in prime-power factorization of C(3n,n).

0, 1, 2, 4, 4, 4, 6, 8, 6, 7, 8, 11, 11, 11, 11, 12, 10, 12, 11, 15, 13, 13, 18, 18, 17, 16, 17, 19, 17, 18, 19, 22, 18, 18, 20, 21, 19, 21, 22, 23, 22, 21, 23, 28, 27, 27, 28, 30, 27, 28, 26, 28, 29, 28, 31, 32, 29, 31, 31, 35, 32, 33, 35, 34, 31, 30, 31, 34, 31, 32, 35, 36, 33, 34, 35, 38, 37, 36, 36

Offset

0,3

Comments

Equivalently, sum of exponents of primes in multinomial coefficient M(3n; n,n,n)/C(2n,n).

Links

Ivan Neretin, Table of n, a(n) for n = 0..10000

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A005809(n)).

a(n) = A022559(3*n) - A022559(2*n) - A022559(n). (End)

Maple

with(numtheory):(combinat):a:=proc(n) if n=0 then 0 else bigomega(binomial(3*n, n)) fi end: seq(a(n), n=0..78); # Zerinvary Lajos, Apr 11 2008

Mathematica

Join[{0}, Table[Total[FactorInteger[Binomial[3 n, n]][[All, 2]]], {n, 78}]] (* Ivan Neretin, Nov 02 2017 *)

Prog

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

Crossrefs

Cf. A001222, A005809, A022559.

Sequence in context: A033825 A235790 A023988 * A201629 A033827 A008217

Adjacent sequences: A023816 A023817 A023818 * A023820 A023821 A023822

Keyword

nonn

Author

Clark Kimberling

Extensions

Edited by N. J. A. Sloane at the suggestion of R. J. Mathar, May 31 2008

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

Status

approved