A023840 Sum of exponents in prime-power factorization of C(5n,n-3).

0, 3, 5, 5, 7, 8, 8, 11, 11, 10, 12, 14, 13, 14, 16, 16, 14, 18, 17, 17, 18, 18, 19, 25, 23, 23, 25, 24, 23, 24, 23, 26, 24, 24, 25, 26, 27, 27, 28, 29, 25, 30, 32, 31, 31, 30, 33, 36, 33, 37, 38, 38, 39, 40, 36, 40, 39, 39, 39, 41, 38, 39, 43, 42, 37, 38, 41, 42, 44, 43, 43, 45, 43, 46, 50, 48, 49

Offset

3,2

Links

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

Formula

From Amiram Eldar, Jun 14 2025: (Start)

a(n) = A001222(A004345(n)).

a(n) = A023838(n) - A001222(4*n+3) + A001222(n-2). (End)

Mathematica

Table[PrimeOmega[Binomial[5 n, n - 3]], {n, 3, 79}] (* Ivan Neretin, Nov 08 2017 *)

Prog

(PARI) a(n) = bigomega(binomial(5*n, n-3)); \\ Amiram Eldar, Jun 14 2025

Crossrefs

Cf. A001222, A004345, A023837, A023838, A023839, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Sequence in context: A393264 A138475 A195990 * A276501 A131421 A088743

Adjacent sequences: A023837 A023838 A023839 * A023841 A023842 A023843

Keyword

nonn

Author

Clark Kimberling

Extensions

Offset corrected to 3 by Ivan Neretin, Nov 08 2017

Status

approved