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Numbers k such that k^2 + 2 is not squarefree.
3

%I #21 Feb 09 2021 02:39:38

%S 4,5,13,14,19,22,23,24,31,32,40,41,49,50,58,59,63,67,68,71,76,77,85,

%T 86,94,95,102,103,104,112,113,121,122,130,131,139,140,148,149,157,158,

%U 166,167,175,176,184,185,193,194,202,203,211,212,218,220,221,223,229

%N Numbers k such that k^2 + 2 is not squarefree.

%C Primes dividing k^2 + 2 at least twice are in A033200. - _Charles R Greathouse IV_, Oct 14 2013

%H Amiram Eldar, <a href="/A227897/b227897.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 4 is in the sequence because 4^2 + 2 = 18 = 2 * 3^2, which is not squarefree.

%e 5 is in the sequence because 5^2 + 2 = 27 = 3^3, which is not squarefree.

%e 6 is not in the sequence because 6^2 + 2 = 38 = 2 * 19, which is squarefree.

%t Select[Range[300], ! SquareFreeQ[#^2 + 2] &] (* _T. D. Noe_, Oct 14 2013 *)

%t (* The following works in Mathematica versions prior to 6.0 *) Select[Range[250], MoebiusMu[#^2 + 2] == 0 &] (* _Alonso del Arte_, Oct 14 2013 *)

%o (PARI) is(n)=!issquarefree(n^2+2) \\ _Charles R Greathouse IV_, Oct 14 2013

%Y Cf. A033200, A013929, A228140.

%K nonn,easy

%O 1,1

%A _Gerasimov Sergey_, Oct 14 2013