A246419 Numbers n such that n^6 - 2 is not squarefree.

10, 22, 50, 143, 204, 267, 311, 312, 423, 455, 461, 479, 506, 556, 579, 600, 649, 818, 845, 889, 987, 1008, 1104, 1108, 1134, 1178, 1258, 1273, 1333, 1343, 1416, 1423, 1467, 1537, 1610, 1637, 1712, 1756, 1779, 2001, 2005, 2045, 2065, 2066, 2104, 2166, 2205

Offset: 1

Author

Mark E. Shoulson, Aug 25 2014

Keywords

• nonn

Examples

			10^6 - 2 = 999998, which is divisible by 16129 = 127^2, so 10 is in the sequence.
11^6 - 2 = 1771559, which is prime, and 12^6 - 2 = 2985982 = 2 * 17 * 31 * 2833 (all prime), so neither of these numbers is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A013928.

Programs

Magma

[n: n in [0..3000] | not IsSquarefree(n^6-2)]; // Vincenzo Librandi, Oct 16 2014

Maple

remove(t -> numtheory:-issqrfree(t^6-2), [$1..3000]); # Robert Israel, Aug 25 2014

Mathematica

Select[Range[2000], MoebiusMu[#^6 - 2] == 0 &] (* Alonso del Arte, Aug 25 2014 *)

PARI

isok(n) = ! issquarefree(n^6-2); \\ Michel Marcus, Oct 11 2014

Python

from sympy import factorint
[i for i in range(1, 500) if any(v>1 for v in factorint(i**6-2).values())]