A110495 Numbers n such that binomial(2n,n) is cubefree.

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, 144, 192, 256, 258, 264, 288, 520, 576, 768, 1056

Offset: 1

Author

T. D. Noe, Jul 22 2005

Keywords

• nonn
• fini
• more

Comments

No others < 15000. This sequence is probably complete. According to Sander, this sequence - and the sequence for any power - is finite.

No more terms < 10^8. - Bert Dobbelaere, Jul 21 2022

Links

• J. W. Sander, A story of binomial coefficients and primes, Amer. Math. Monthly 102 (1995), 802-807.

Crossrefs

Cf. A110496 (least k such that prime(n)^3 divides binomial(2k, k)).

Programs

Mathematica

t3=Table[f=FactorInteger[Binomial[2n, n]]; s=Select[f, #[[2]]>2&]; If[s=={}, 0, s[[ -1, 1]]], {n, 15000}]; Flatten[Position[t3, 0]]

PARI

isok(n) = vecmax(factor(binomial(2*n, n))[,2]) < 3; \\ Michel Marcus, Oct 04 2017