This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A023853 #31 Jun 12 2025 08:15:39
%S A023853 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,
%T A023853 26,29,31,29,31,32,35,31,31,31,35,33,35,37,36,36,37,39,43,42,43,46,47,
%U A023853 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
%N A023853 Sum of exponents in prime-power factorization of binomial(6n, 2n).
%H A023853 Ivan Neretin, <a href="/A023853/b023853.txt">Table of n, a(n) for n = 0..10000</a>
%F A023853 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023853 a(n) = A001222(3*A259613(n)) for n >= 1.
%F A023853 a(n) = A022559(6*n) - A022559(4*n) - A022559(2*n). (End)
%t A023853 Join[{0}, Table[Total[Transpose[FactorInteger[Binomial[6 n,2 n]]] [[2]]],{n,80}]] (* _Harvey P. Dale_, Jun 28 2011 *)
%t A023853 a[n_] := PrimeOmega[Binomial[6*n, 2*n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023853 (PARI) a(n) = bigomega(binomial(6*n, 2*n)); \\ _Amiram Eldar_, Jun 11 2025
%Y A023853 Cf. A001222, A022559, A259613.
%Y A023853 Cf. A023852, A023854.
%K A023853 nonn
%O A023853 0,2
%A A023853 _Clark Kimberling_
%E A023853 a(0)=0 inserted by _Amiram Eldar_, Jun 11 2025