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 A110496 Least k such that prime(n)^3 divides binomial(2k,k). 3
 7, 14, 63, 172, 666, 1099, 2457, 3430, 6084, 12195, 14896, 25327, 34461, 39754, 51912, 74439, 102690, 113491, 150382, 178956, 194509, 246520, 285894, 352485, 456337, 515151, 546364, 612522, 647515, 721449, 1024192, 1124046, 1285677 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For prime p > (2n)^(1/3), p^3 does not divide binomial(2n,n). LINKS Chai Wah Wu, Table of n, a(n) for n = 1..100 FORMULA a(n) = (prime(n)^3 + 1)/2 for n>1. Product_{n>=1} (1 - 1/a(n)) = (54/49)*zeta(6)/zeta(3)^2. - Amiram Eldar, Jun 08 2022 MATHEMATICA 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]]}] lst={7}; Do[AppendTo[lst, (DivisorSigma[3, Prime[n]])/2], {n, 2, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *) CROSSREFS Cf. A000984, A030078. Cf. A110495 (binomial(2k, k) is cubefree). Sequence in context: A241201 A295388 A020700 * A117867 A291008 A196254 Adjacent sequences: A110493 A110494 A110495 * A110497 A110498 A110499 KEYWORD nonn AUTHOR T. D. Noe, Jul 22 2005 STATUS approved

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Last modified February 4 02:26 EST 2023. Contains 360045 sequences. (Running on oeis4.)