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 A110496 #21 Jul 14 2025 11:37:32
%S A110496 7,14,63,172,666,1099,2457,3430,6084,12195,14896,25327,34461,39754,
%T A110496 51912,74439,102690,113491,150382,178956,194509,246520,285894,352485,
%U A110496 456337,515151,546364,612522,647515,721449,1024192,1124046,1285677
%N A110496 Least k such that prime(n)^3 divides binomial(2k,k).
%C A110496 For prime p > (2n)^(1/3), p^3 does not divide binomial(2n,n).
%H A110496 Chai Wah Wu, <a href="/A110496/b110496.txt">Table of n, a(n) for n = 1..100</a>
%F A110496 a(n) = (prime(n)^3 + 1)/2 = (1+A030078(n))/2 for n>1.
%F A110496 Product_{n>=1} (1 - 1/a(n)) = (54/49)*zeta(6)/zeta(3)^2. - _Amiram Eldar_, Jun 08 2022
%t A110496 t3=Table[f=FactorInteger[Binomial[2n, n]]; s=Select[f, #[[2]]>2&]; If[s=={}, 0, s[[ -1, 1]]], {n, 15000}]; Table[p=Prime[i]; First[Flatten[Position[t3, p]]], {i, PrimePi[Max[t3]]}]
%t A110496 lst={7};Do[AppendTo[lst,(DivisorSigma[3,Prime[n]])/2],{n,2,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 11 2009 *)
%Y A110496 Cf. A000984, A030078.
%Y A110496 Cf. A110495 (binomial(2k, k) is cubefree).
%K A110496 nonn
%O A110496 1,1
%A A110496 _T. D. Noe_, Jul 22 2005