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 A023854 #28 Jun 12 2025 08:16:13
%S A023854 0,3,5,6,7,11,11,12,13,14,15,16,15,19,20,21,22,23,23,22,25,29,25,29,
%T A023854 28,31,32,30,31,34,34,35,35,36,36,38,38,41,41,41,40,46,44,43,44,44,46,
%U A023854 47,46,47,50,51,49,53,49,52,53,53,56,55,56,60,60,61,57,61,61,61,65,66,63,67,66,69,69,66,69,71,70,72,72
%N A023854 Sum of exponents in prime-power factorization of binomial(6n, 3n).
%H A023854 Ivan Neretin, <a href="/A023854/b023854.txt">Table of n, a(n) for n = 0..10000</a>
%F A023854 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023854 a(n) = A001222(A066802(n)).
%F A023854 a(n) = A022559(6*n) - 2*A022559(3*n). (End)
%t A023854 Join[{0}, Total[Transpose[FactorInteger[Binomial[6 #, 3 #]]][[2]]]&/@Range[80]] (* _Harvey P. Dale_, May 14 2011 *)
%t A023854 a[n_] := PrimeOmega[Binomial[6*n, 3*n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023854 (PARI) a(n) = bigomega(binomial(6*n, 3*n)); \\ _Amiram Eldar_, Jun 11 2025
%Y A023854 Cf. A001222, A022559, A023852, A023853, A066802.
%K A023854 nonn
%O A023854 0,2
%A A023854 _Clark Kimberling_
%E A023854 Corrected and extended by _Harvey P. Dale_, May 14 2011
%E A023854 a(0)=0 inserted by _Amiram Eldar_, Jun 11 2025