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

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, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 80, 82, 84, 86, 87, 88, 89, 90

Offset: 1

Author

Michel Marcus, Mar 04 2017

Keywords

• nonn

Comments

Zang & Li prove that this sequence is infinite.

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Min Zhang and Jinjiang Li, Distribution of cube-free numbers with form [n^c], Frontiers of Mathematics in China, Vol. 12 (2017), pp. 1515-1525; arXiv preprint, arXiv:1702.00165 [math.NT], 2017.

Crossrefs

Cf. A000093, A004709, A088453, A283295.

Programs

Mathematica

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

PARI

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