A227897 Numbers k such that k^2 + 2 is not squarefree.

4, 5, 13, 14, 19, 22, 23, 24, 31, 32, 40, 41, 49, 50, 58, 59, 63, 67, 68, 71, 76, 77, 85, 86, 94, 95, 102, 103, 104, 112, 113, 121, 122, 130, 131, 139, 140, 148, 149, 157, 158, 166, 167, 175, 176, 184, 185, 193, 194, 202, 203, 211, 212, 218, 220, 221, 223, 229

Offset: 1

Author

Gerasimov Sergey, Oct 14 2013

Keywords

• nonn
• easy

Comments

Primes dividing k^2 + 2 at least twice are in A033200. - Charles R Greathouse IV, Oct 14 2013

Examples

			4 is in the sequence because 4^2 + 2 = 18 = 2 * 3^2, which is not squarefree.
5 is in the sequence because 5^2 + 2 = 27 = 3^3, which is not squarefree.
6 is not in the sequence because 6^2 + 2 = 38 = 2 * 19, which is squarefree.
		

Links

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

Crossrefs

Cf. A033200, A013929, A228140.

Programs

Mathematica

Select[Range[300], ! SquareFreeQ[#^2 + 2] &] (* T. D. Noe, Oct 14 2013 *)
(* The following works in Mathematica versions prior to 6.0 *) Select[Range[250], MoebiusMu[#^2 + 2] == 0 &] (* Alonso del Arte, Oct 14 2013 *)

PARI

is(n)=!issquarefree(n^2+2) \\ Charles R Greathouse IV, Oct 14 2013

Formula

{k: k^2 + 2 is in A013929}.