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

1,2

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

Table of n, a(n) for n=1..35.

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)).

Sequence in context: A337800 A091902 A067698 * A052347 A193299 A022773

Adjacent sequences: A110492 A110493 A110494 * A110496 A110497 A110498

Keyword

nonn,fini,more

Author

T. D. Noe, Jul 22 2005

Status

approved