cp's OEIS Frontend

A283296 Integers n such that floor(n^(3/2)) is cubefree.

%I A283296 #13 Feb 17 2021 03:58:23
%S A283296 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 A283296 31,32,34,35,37,38,40,41,43,44,45,46,47,48,50,51,52,53,54,55,56,57,58,
%U A283296 59,61,65,67,69,70,71,72,73,74,75,76,80,82,84,86,87,88,89,90
%N A283296 Integers n such that floor(n^(3/2)) is cubefree.
%C A283296 Zang & Li prove that this sequence is infinite.
%C A283296 The asymptotic density of this sequence is 1/zeta(3) (A088453) (Zang and Li, 2017). - _Amiram Eldar_, Feb 17 2021
%H A283296 Charles R Greathouse IV, <a href="/A283296/b283296.txt">Table of n, a(n) for n = 1..10000</a>
%H A283296 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 A283296 Select[Range[90], Max[FactorInteger[Floor[#^(3/2)]][[All, 2]]] < 3&] (* _Jean-François Alcover_, Feb 23 2019 *)
%o A283296 (PARI) isok(n) = if (n < 4, 1, vecmax(factor(sqrtint(n^3))[,2]) < 3);
%Y A283296 Cf. A000093, A004709, A088453, A283295.
%K A283296 nonn
%O A283296 1,2
%A A283296 _Michel Marcus_, Mar 04 2017