A023846 Sum of exponents in prime-power factorization of binomial(5n, n+4).

0, 4, 5, 6, 6, 8, 10, 10, 10, 11, 12, 13, 15, 14, 14, 16, 15, 17, 16, 20, 19, 18, 18, 20, 19, 22, 25, 22, 23, 25, 24, 26, 24, 25, 24, 26, 25, 27, 30, 30, 28, 31, 29, 29, 31, 29, 31, 33, 32, 33, 33, 37, 36, 38, 39, 40, 38, 42, 40, 41, 40, 39, 39, 40, 39, 40, 39, 40, 43, 41, 43, 47, 43, 45, 47, 45, 46

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

By Kummer's theorem, a(n) is the sum over all primes p of the number of carries when n+4 is added to 4n-4 in base p. - Robert Israel, Nov 09 2017

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Wikipedia, Kummer's theorem.

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023847, A023848, A023849, A023850, A023851.

Programs

Maple

seq(numtheory:-bigomega(binomial(5*n,n+4)), n=1..100); # Robert Israel, Nov 09 2017

Mathematica

Table[PrimeOmega[Binomial[5 n, n + 4]], {n, 77}] (* Ivan Neretin, Nov 09 2017 *)

PARI

a(n) = bigomega(binomial(5*n, n+4)); \\ Michel Marcus, Nov 09 2017

Formula

a(n) = A023844(n) + A001222(4*n-3) - A001222(n+4). - Amiram Eldar, Jun 14 2025