A023853 Sum of exponents in prime-power factorization of binomial(6n, 2n).
0, 2, 4, 6, 6, 8, 11, 11, 10, 11, 13, 18, 17, 17, 17, 19, 18, 20, 19, 22, 22, 23, 27, 28, 27, 26, 29, 31, 29, 31, 32, 35, 31, 31, 31, 35, 33, 35, 37, 36, 36, 37, 39, 43, 42, 43, 46, 47, 43, 44, 45, 48, 47, 46, 50, 53, 51, 52, 53, 57, 55, 55, 56, 56, 51, 52, 54, 56, 56, 55, 58, 62, 58, 59, 60, 61, 62
Offset: 0
Keywords
Links
- Ivan Neretin, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
Join[{0}, Table[Total[Transpose[FactorInteger[Binomial[6 n,2 n]]] [[2]]],{n,80}]] (* Harvey P. Dale, Jun 28 2011 *) a[n_] := PrimeOmega[Binomial[6*n, 2*n]]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2025 *) -
PARI
a(n) = bigomega(binomial(6*n, 2*n)); \\ Amiram Eldar, Jun 11 2025
Formula
Extensions
a(0)=0 inserted by Amiram Eldar, Jun 11 2025