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 A023833 #12 Jun 13 2025 07:45:26
%S A023833 0,4,5,7,6,8,8,11,11,12,11,12,10,15,13,17,15,17,16,18,18,20,17,20,19,
%T A023833 21,21,21,18,22,20,26,22,26,25,27,25,28,28,30,29,31,30,31,28,28,27,33,
%U A023833 30,33,31,33,30,35,30,34,33,35,36,35,33,37,37,42,38,41,39,42,41,44,39,45,42,45,46,45,44
%N A023833 Sum of exponents in prime-power factorization of C(4n,n+3).
%H A023833 Ivan Neretin, <a href="/A023833/b023833.txt">Table of n, a(n) for n = 1..10000</a>
%F A023833 a(n) = A023832(n) - A001222(3*n-2) + A001222(n+3). - _Amiram Eldar_, Jun 13 2025
%t A023833 Join[{0},Total[Transpose[FactorInteger[#]][[2]]]&/@Table[Binomial[4n,n+3],{n,2,80}]] (* _Harvey P. Dale_, Dec 24 2014 *)
%t A023833 a[n_] := PrimeOmega[Binomial[4*n, n+3]]; Array[a, 100] (* _Amiram Eldar_, Jun 13 2025 *)
%o A023833 (PARI) a(n) = bigomega(binomial(4*n,n+3)); \\ _Amiram Eldar_, Jun 13 2025
%Y A023833 Cf. A001222, A023826, A023827, A023828, A023829, A023830, A023831, A023832, A023834, A023835, A023836.
%K A023833 nonn
%O A023833 1,2
%A A023833 _Clark Kimberling_