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 A023816 #21 Jun 12 2025 08:09:28
%S A023816 0,1,2,3,3,5,5,6,6,6,6,8,7,9,11,11,9,11,11,12,12,12,12,15,13,14,15,14,
%T A023816 14,16,15,16,15,16,16,17,15,16,18,19,17,21,20,22,22,21,22,24,22,22,23,
%U A023816 23,22,25,23,23,22,22,23,26,25,27,28,29,25,26,25,27,29,29,28,30,28,30,32,31,30,32,32,33
%N A023816 Sum of exponents in prime-power factorization of C(2n,n).
%H A023816 Ivan Neretin, <a href="/A023816/b023816.txt">Table of n, a(n) for n = 0..10000</a>
%F A023816 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023816 a(n) = A001222(A000984(n)).
%F A023816 a(n) = A022559(2*n) - 2*A022559(n). (End)
%p A023816 with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(2*n,n)) fi end: seq(a(n), n=0..79); # _Zerinvary Lajos_, Apr 11 2008
%t A023816 Join[{0},Table[Total[FactorInteger[Binomial[2 n, n]][[All, 2]]], {n, 79}]] (* _Ivan Neretin_, Oct 26 2017 *)
%o A023816 (PARI) a(n) = bigomega(binomial(2*n, n)); \\ _Amiram Eldar_, Jun 11 2025
%Y A023816 Cf. A000984, A001222, A022559.
%K A023816 nonn
%O A023816 0,3
%A A023816 _Clark Kimberling_
%E A023816 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025