A283295 Integers n such that floor(n^(3/2)) is squarefree.

1, 2, 3, 5, 6, 8, 10, 12, 13, 15, 17, 19, 20, 22, 23, 32, 41, 43, 44, 45, 46, 47, 50, 52, 53, 55, 56, 57, 59, 69, 71, 72, 73, 75, 76, 80, 82, 84, 86, 87, 89, 90, 94, 97, 98, 99, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 122, 125

Offset: 1

Author

Michel Marcus, Mar 04 2017

Keywords

• nonn

Comments

Cao & Zhai prove that this sequence is infinite.

The asymptotic density of this sequence is 6/Pi^2 (A059956) (Cao and Zhai, 1998). - Amiram Eldar, Feb 17 2021

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Xiaodong Cao and Wenguang Zhai, The distribution of square-free numbers of the form [n^c], Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 2 , p. 287-299.

Crossrefs

Cf. A000093, A005117, A059956, A283296.

Programs

Mathematica

Select[Range[200],SquareFreeQ[Floor[#^(3/2)]]&] (* Harvey P. Dale, Aug 25 2017 *)

PARI

isok(n) = issquarefree(sqrtint(n^3));