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 A023824 #18 Jun 12 2025 08:13:40
%S A023824 0,2,4,5,5,6,6,8,8,8,11,13,11,11,11,12,12,13,13,15,14,17,17,19,16,16,
%T A023824 20,19,18,18,18,23,19,18,21,22,20,22,23,24,23,24,26,28,29,27,27,30,27,
%U A023824 28,28,29,27,31,30,32,32,31,35,36,32,31,33,34,31,32,33,34,32,34,34,38,33,35,38,37,38,36,33
%N A023824 Sum of exponents in prime-power factorization of C(3n,n+2).
%H A023824 Ivan Neretin, <a href="/A023824/b023824.txt">Table of n, a(n) for n = 1..10000</a>
%F A023824 a(n) = A023823(n) + A001222(2*n-1) - A001222(n+2). - _Amiram Eldar_, Jun 12 2025
%e A023824 For n = 4, C(12,6) = 924 = 2^2*3*7*11, so a(4) = 2+1+1+1 = 5.
%t A023824 Table[Total[FactorInteger[Binomial[3n,n+2]][[All,2]]],{n,2,80}] (* _Harvey P. Dale_, Dec 24 2016 *)
%t A023824 a[n_] := PrimeOmega[Binomial[3*n, n+2]]; Array[a, 100] (* _Amiram Eldar_, Jun 12 2025 *)
%o A023824 (PARI) a(n) = bigomega(binomial(3*n, n+2)); \\ _Amiram Eldar_, Jun 12 2025
%Y A023824 Cf. A001222, A023819, A023820, A023821, A023822, A023824, A023825.
%K A023824 nonn
%O A023824 1,2
%A A023824 _Clark Kimberling_
%E A023824 a(1)=0 added by _Ivan Neretin_, Nov 02 2017