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 A023830 #25 Jun 13 2025 07:45:13
%S A023830 0,3,4,6,6,10,8,8,8,11,12,12,13,14,15,16,12,16,15,17,18,21,17,20,19,
%T A023830 19,22,19,21,25,25,26,23,25,25,26,26,28,25,27,25,29,28,27,31,32,31,33,
%U A023830 30,30,31,31,31,34,32,33,32,35,35,37,39,42,42,41,37,40,41,38,42,44,40,46,42,45,46,45,44
%N A023830 Sum of exponents in prime-power factorization of C(4n,n-4).
%H A023830 Ivan Neretin, <a href="/A023830/b023830.txt">Table of n, a(n) for n = 4..10000</a>
%F A023830 a(n) = Omega( C(4n,n-4) ) = A001222( C(4n,n-4) ), n > 3.
%F A023830 From _Amiram Eldar_, Jun 13 2025 (Start)
%F A023830 a(n) = A001222(A004334(n)).
%F A023830 a(n) = A023829(n) - A001222(3*n+4) + A001222(n-3). (End)
%p A023830 with(numtheory): A023830:=n->bigomega(binomial(4*n,n-4)): seq(A023830(n), n=4..100); # _Wesley Ivan Hurt_, Oct 13 2014
%t A023830 Join[{0},Table[Total[Transpose[FactorInteger[Binomial[4n,n-4]]][[2]]],{n,5,80}]] (* _Harvey P. Dale_, Oct 12 2014 *)
%t A023830 a[n_] := PrimeOmega[Binomial[4*n, n-4]]; Array[a, 100, 4] (* _Amiram Eldar_, Jun 13 2025 *)
%o A023830 (PARI) a(n) = bigomega(binomial(4*n, n-4)); \\ _Michel Marcus_, Oct 12 2014
%Y A023830 Cf. A001222, A004334, A023826, A023827, A023828, A023829, A023831, A023832, A023833, A023834, A023835, A023836.
%K A023830 nonn
%O A023830 4,2
%A A023830 _Clark Kimberling_
%E A023830 Offset changed by _Wesley Ivan Hurt_, Oct 13 2014