A173186 Numbers k such that k^2-1 is not squarefree.

1, 3, 5, 7, 8, 9, 10, 11, 13, 15, 17, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 57, 59, 61, 62, 63, 64, 65, 67, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 87, 89, 91, 93, 95, 97, 98, 99, 100, 101, 103, 105

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 12 2010

Keywords

• nonn

Comments

Complement of A067874 - R. J. Mathar, Feb 13 2010

The asymptotic density of this sequence is 1 - Product_{p prime} (1 - 2/p^2) = 0.677365... (1 - A065474). - Amiram Eldar, Feb 25 2021

Examples

			5 is a term since 5^2-1 = 24 = 2^3*3 is not squarefree.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013929, A065474, A067874.

Programs

Mathematica

f[n_]:=SquareFreeQ[n]; lst={};Do[If[f[n^2-1],AppendTo[lst,n]],{n,6!}]; lst
Select[Range[120],!SquareFreeQ[#^2-1]&] (* Harvey P. Dale, Jul 16 2016 *)

Extensions

Definition edited by R. J. Mathar, Feb 13 2010