cp's OEIS Frontend

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.

A023835 Sum of exponents in prime-power factorization of C(4n,2n-1).

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%I A023835 #11 Jun 13 2025 07:45:29
%S A023835 2,4,6,7,7,9,11,12,13,13,13,15,14,16,17,18,16,18,18,20,22,22,23,25,24,
%T A023835 24,25,24,24,28,27,29,27,30,30,32,31,31,34,32,31,33,34,37,36,35,36,40,
%U A023835 37,37,38,39,39,42,41,42,42,42,42,43,44,46,47,48,45,46,44,45,48,49,47,50,47,49,53,52,51
%N A023835 Sum of exponents in prime-power factorization of C(4n,2n-1).
%H A023835 Ivan Neretin, <a href="/A023835/b023835.txt">Table of n, a(n) for n = 1..10000</a>
%F A023835 a(n) = A023832(n) - A001222(2*n+1) + A001222(2*n) = A023832(n) - A076191(2*n). - _Amiram Eldar_, Jun 13 2025
%t A023835 Table[PrimeOmega[Binomial[4 n, 2 n - 1]], {n, 78}] (* _Ivan Neretin_, Nov 08 2017 *)
%o A023835 (PARI) a(n) = bigomega(binomial(4*n,2*n-1)); \\ _Amiram Eldar_, Jun 13 2025
%Y A023835 Cf. A001222, A023826, A023827, A023828, A023829, A023830, A023831, A023832, A023834, A023836, A076191.
%K A023835 nonn
%O A023835 1,1
%A A023835 _Clark Kimberling_
%E A023835 a(74)-a(77) corrected by _Ivan Neretin_, Nov 08 2017