A023837 Sum of exponents in prime-power factorization of C(5n,n).

0, 1, 3, 3, 4, 6, 7, 8, 8, 7, 9, 12, 11, 14, 13, 14, 12, 15, 14, 15, 18, 17, 17, 19, 18, 17, 23, 22, 21, 25, 23, 26, 21, 23, 22, 24, 23, 24, 27, 27, 27, 27, 29, 27, 28, 31, 30, 33, 28, 31, 32, 33, 36, 38, 36, 38, 37, 35, 39, 40, 41, 41, 41, 39, 34, 38, 38, 38, 39, 41, 39, 46, 41, 43, 45, 43, 45, 48, 47

Offset

0,3

Links

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

Formula

a(n) = A001222(A001449(n)). - Amiram Eldar, Jun 14 2025

Maple

with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(5*n, n)) fi end: seq(a(n), n=0..78); # Zerinvary Lajos, Apr 11 2008

Mathematica

Table[PrimeOmega[Binomial[5 n, n]], {n, 0, 78}] (* Ivan Neretin, Nov 08 2017 *)

Prog

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

Crossrefs

Cf. A001222, A001449, A023838, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Sequence in context: A161019 A137901 A138095 * A393546 A240115 A196249

Adjacent sequences: A023834 A023835 A023836 * A023838 A023839 A023840

Keyword

nonn

Author

Clark Kimberling

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 14 2025

Status

approved