A023817 -id:A023817 - cp's OEIS frontend

A023836 Sum of exponents in prime-power factorization of C(4n,2n-2).

0, 3, 4, 6, 6, 8, 8, 11, 11, 12, 11, 14, 13, 16, 13, 17, 14, 18, 15, 19, 20, 21, 21, 23, 23, 22, 22, 24, 22, 27, 22, 29, 26, 28, 27, 31, 29, 31, 31, 31, 31, 32, 32, 35, 34, 35, 32, 39, 34, 37, 35, 38, 37, 40, 37, 41, 40, 42, 40, 43, 43, 44, 43, 46, 43, 45, 42, 46, 45, 48, 43, 50, 46, 48, 50, 50, 50

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A001222, A023817, A023826, A023827, A023828, A023829, A023830, A023831, A023832, A023834, A023835.

Join[{0},Rest[Total[Last[Transpose[FactorInteger[#]]]]&/@(Binomial[ 4#,2#-2]&/@Range[80])]] (* Harvey P. Dale, Jun 07 2011 *)
a[n_] := PrimeOmega[Binomial[4*n, 2*n-2]]; Array[a, 100] (* Amiram Eldar, Jun 13 2025 *)

a(n) = bigomega(binomial(4*n,2*n-2)); \\ Amiram Eldar, Jun 13 2025

From Amiram Eldar, Jun 13 2025: (Start)
a(n) = A023817(2*n).
a(n) = A023835(n) - A001222(2*n+2) + A001222(2*n-1). (End)

A023818 Sum of exponents in prime-power factorization of C(2n,n-2).

Original entry on oeis.org

0, 2, 3, 5, 4, 4, 6, 8, 6, 7, 8, 9, 8, 10, 11, 12, 11, 11, 12, 14, 11, 12, 14, 15, 13, 15, 16, 16, 13, 13, 17, 19, 14, 16, 18, 17, 15, 18, 19, 22, 20, 20, 21, 24, 21, 20, 23, 24, 23, 24, 22, 23, 22, 23, 24, 25, 22, 24, 27, 27, 22, 26, 29, 30, 26, 26, 28, 30, 27, 28, 31, 31, 29, 31, 31, 33, 31, 28, 31

Offset: 2

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 2..10000

Cf. A001222, A002694, A023816, A023817.

Join[{0}, Table[Total[FactorInteger[Binomial[2 n, n - 2]][[All, 2]]], {n, 3, 80}]] (* Ivan Neretin, Nov 02 2017 *)
a[n_] := PrimeOmega[Binomial[2*n, n-2]]; Array[a, 100, 2] (* Amiram Eldar, Jun 12 2025 *)

a(n) = bigomega(binomial(2*n, n-2)); \\ Amiram Eldar, Jun 12 2025

From Amiram Eldar, Jun 12 2025: (Start)
a(n) = A001222(A002694(n)).
a(n) = A023817(n) - A022559(n+2) + A022559(n-1). (End)

Offset corrected to 2 by Ivan Neretin, Nov 02 2017

cp's OEIS Frontend

A023836 Sum of exponents in prime-power factorization of C(4n,2n-2).

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