A228140 -id:A228140 - cp's OEIS frontend

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

Gerasimov Sergey, Oct 14 2013

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

			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.

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

Cf. A033200, A013929, A228140.

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 *)

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

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

A247096 Numbers n such that (n^2 - 2) and (n^2 + 2) are not squarefree.

Original entry on oeis.org

58, 59, 157, 284, 338, 373, 382, 500, 598, 725, 745, 823, 843, 941, 1039, 1111, 1166, 1201, 1264, 1382, 1400, 1480, 1490, 1607, 1705, 1732, 1823, 1921, 1999, 2038, 2048, 2146, 2264, 2272, 2362, 2489, 2587, 2686, 2705, 2767, 2803, 2930, 3028, 3146, 3244, 3371, 3469, 3547, 3587, 3685, 3712

Offset: 1

Juri-Stepan Gerasimov, Nov 18 2014

nonn

Intersection of A227897 and A228140.

Primes: 59, 157, 373, 823, 941, 1039, 1201, 1607, 1823, 1999, 2767, 2803, 3371, 3469, 3547, ...

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A227897, A228140.

[n: n in [1..4000] | not IsSquarefree(n^2 - 2) and not IsSquarefree(n^2 + 2)];

Select[Range[4000],! SquareFreeQ[#^2 - 2] && ! SquareFreeQ[#^2 + 2] &] (* Vincenzo Librandi, Nov 18 2014 *)

select(n->!issquarefree(n^2-2) && !issquarefree(n^2+2), vector(4000, n, n)) \\ Colin Barker, Nov 18 2014

cp's OEIS Frontend

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

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