A110495 - OEIS

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

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OFFSET

1,2

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.

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]]

PROG

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

CROSSREFS

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

KEYWORD

nonn,fini,more

AUTHOR

T. D. Noe, Jul 22 2005

STATUS

approved