A023987 Sum of exponents of primes in C(5n,3n) - sum of exponents of primes in C(3n,2n).

0, 1, 2, 0, 2, 4, 2, 3, 5, 4, 5, 2, 2, 7, 5, 5, 7, 7, 7, 3, 9, 11, 3, 5, 6, 8, 11, 7, 9, 12, 10, 10, 10, 12, 11, 10, 13, 14, 13, 13, 14, 15, 14, 5, 8, 11, 8, 9, 9, 12, 14, 13, 16, 20, 12, 14, 17, 14, 19, 12, 17, 19, 17, 15, 15, 21, 20, 16, 19, 23, 16, 21, 21, 23, 22, 17, 22, 26, 24, 24, 26, 26, 24, 22, 23

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A022559, A023819, A023847.

Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023990, A023991, A023992, A023993.

Programs

Mathematica

a[n_] := PrimeOmega[Binomial[5*n, 3*n]] - PrimeOmega[Binomial[3*n, 2*n]]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2025 *)

PARI

a(n) = bigomega(binomial(5*n, 3*n)) - bigomega(binomial(3*n, 2*n)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A023847(n) - A023819(n).

a(n) = A022559(5*n) - 2*A022559(3*n) + A022559(n). (End)

Extensions

Name clarified, offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 11 2025