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

0,3

Links

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

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A001222, A022559, A023819, A023847.

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

Sequence in context: A223487 A226911 A291956 * A021498 A025251 A193334

Adjacent sequences: A023984 A023985 A023986 * A023988 A023989 A023990

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved