

A110495


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


3



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

Table of n, a(n) for n=1..35.
J. W. Sander, A story of binomial coefficients and primes, Amer. Math. Monthly 102 (1995), 802807.


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



