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 A023838 #12 Jun 14 2025 04:18:19
%S A023838 0,2,3,5,5,7,8,9,8,10,10,12,14,13,15,14,14,16,14,17,17,18,18,21,18,22,
%T A023838 24,23,23,24,24,24,23,23,24,25,24,26,28,29,25,30,27,29,33,30,30,32,32,
%U A023838 33,33,37,37,38,38,37,36,40,39,44,39,41,40,39,37,39,38,39,42,41,44,44,43,43,44,46,48,49
%N A023838 Sum of exponents in prime-power factorization of C(5n,n-1).
%H A023838 Ivan Neretin, <a href="/A023838/b023838.txt">Table of n, a(n) for n = 1..10000</a>
%F A023838 From _Amiram Eldar_, Jun 14 2025: (Start)
%F A023838 a(n) = A001222(A004343(n)).
%F A023838 a(n) = A023837(n) - A001222(4*n+1) + A001222(n). (End)
%t A023838 Join[{0},Table[Total[Transpose[FactorInteger[Binomial[5 n,n-1]]] [[2]]],{n,2,80}]] (* _Harvey P. Dale_, Dec 31 2012 *)
%t A023838 a[n_] := PrimeOmega[Binomial[5*n, n-1]]; Array[a, 100] (* _Amiram Eldar_, Jun 14 2025 *)
%o A023838 (PARI) a(n) = bigomega(binomial(5*n,n-1)); \\ _Amiram Eldar_, Jun 14 2025
%Y A023838 Cf. A001222, A004343, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.
%K A023838 nonn
%O A023838 1,2
%A A023838 _Clark Kimberling_