# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a110495 Showing 1-1 of 1 %I A110495 #13 Jul 21 2022 05:31:21 %S A110495 1,2,3,4,5,6,8,9,10,12,16,18,20,24,32,33,34,36,40,48,65,66,72,96,136, %T A110495 144,192,256,258,264,288,520,576,768,1056 %N A110495 Numbers n such that binomial(2n,n) is cubefree. %C A110495 No others < 15000. This sequence is probably complete. According to Sander, this sequence - and the sequence for any power - is finite. %C A110495 No more terms < 10^8. - _Bert Dobbelaere_, Jul 21 2022 %H A110495 J. W. Sander, A story of binomial coefficients and primes, Amer. Math. Monthly 102 (1995), 802-807. %t A110495 t3=Table[f=FactorInteger[Binomial[2n, n]]; s=Select[f, #[[2]]>2&]; If[s=={}, 0, s[[ -1, 1]]], {n, 15000}]; Flatten[Position[t3, 0]] %o A110495 (PARI) isok(n) = vecmax(factor(binomial(2*n, n))[,2]) < 3; \\ _Michel Marcus_, Oct 04 2017 %Y A110495 Cf. A110496 (least k such that prime(n)^3 divides binomial(2k, k)). %K A110495 nonn,fini,more %O A110495 1,2 %A A110495 _T. D. Noe_, Jul 22 2005 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE