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

1,2

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A013929, A065474, A067874.

Sequence in context: A247459 A020491 A168501 * A335575 A047746 A111638

Adjacent sequences: A173183 A173184 A173185 * A173187 A173188 A173189

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 12 2010

Extensions

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

Status

approved