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Integers n such that floor(n^(3/2)) is cubefree.
2

%I #13 Feb 17 2021 03:58:23

%S 1,2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,22,23,24,26,27,28,29,30,

%T 31,32,34,35,37,38,40,41,43,44,45,46,47,48,50,51,52,53,54,55,56,57,58,

%U 59,61,65,67,69,70,71,72,73,74,75,76,80,82,84,86,87,88,89,90

%N Integers n such that floor(n^(3/2)) is cubefree.

%C Zang & Li prove that this sequence is infinite.

%C The asymptotic density of this sequence is 1/zeta(3) (A088453) (Zang and Li, 2017). - _Amiram Eldar_, Feb 17 2021

%H Charles R Greathouse IV, <a href="/A283296/b283296.txt">Table of n, a(n) for n = 1..10000</a>

%H Min Zhang and Jinjiang Li, <a href="https://doi.org/10.1007/s11464-017-0652-1">Distribution of cube-free numbers with form [n^c]</a>, Frontiers of Mathematics in China, Vol. 12 (2017), pp. 1515-1525; <a href="https://arxiv.org/abs/1702.00165">arXiv preprint</a>, arXiv:1702.00165 [math.NT], 2017.

%t Select[Range[90], Max[FactorInteger[Floor[#^(3/2)]][[All, 2]]] < 3&] (* _Jean-François Alcover_, Feb 23 2019 *)

%o (PARI) isok(n) = if (n < 4, 1, vecmax(factor(sqrtint(n^3))[,2]) < 3);

%Y Cf. A000093, A004709, A088453, A283295.

%K nonn

%O 1,2

%A _Michel Marcus_, Mar 04 2017