A023829 Sum of exponents in prime-power factorization of C(4n,n-3).

0, 4, 3, 5, 6, 8, 9, 9, 6, 10, 10, 13, 11, 15, 14, 15, 13, 17, 14, 17, 15, 19, 20, 18, 18, 21, 19, 21, 17, 24, 23, 26, 22, 26, 25, 25, 24, 28, 27, 26, 25, 28, 27, 29, 26, 31, 31, 33, 29, 34, 28, 31, 30, 33, 33, 32, 30, 34, 35, 37, 34, 42, 41, 41, 37, 40, 38, 42, 37, 44, 42, 41, 42, 45, 45, 46, 43, 45

Offset

3,2

Links

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

Formula

From Amiram Eldar, Jun 13 2025 (Start)

a(n) = A001222(A004333(n)).

a(n) = A023828(n) - A001222(3*n+3) + A001222(n-2). (End)

Mathematica

Table[PrimeOmega[Binomial[4 n, n - 3]], {n, 3, 78}] (* Ivan Neretin, Nov 02 2017 *)

Prog

(PARI) a(n) = bigomega(binomial(4*n, n-3)); \\ Amiram Eldar, Jun 13 2025

Crossrefs

Cf. A001222, A004333, A023826, A023827, A023828, A023830, A023831, A023832, A023833, A023834, A023835, A023836.

Sequence in context: A226211 A296413 A016701 * A335583 A328109 A000211

Adjacent sequences: A023826 A023827 A023828 * A023830 A023831 A023832

Keyword

nonn

Author

Clark Kimberling

Extensions

Offset corrected to 3 by Ivan Neretin, Nov 02 2017

Status

approved