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Numbers k such that k^2 + 1 and k^2 - 1 are not squarefree.
1

%I #27 Sep 08 2022 08:45:09

%S 7,41,43,57,82,93,99,107,117,118,143,157,168,193,207,239,243,251,257,

%T 293,307,327,332,343,357,368,393,407,437,443,457,493,507,515,532,540,

%U 543,557,568,577,593,606,607,643,657,693,707,743,746,757,775,776,782

%N Numbers k such that k^2 + 1 and k^2 - 1 are not squarefree.

%C This sequence is infinite. For instance, it contains all numbers of the form 100*m + 7. - _Emmanuel Vantieghem_, Oct 25 2016

%H Amiram Eldar, <a href="/A080666/b080666.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[10^3], ! SquareFreeQ[ #^2 - 1] && ! SquareFreeQ[ #^2 + 1] &]

%o (Magma) [n : n in [2..800] | not IsSquarefree(n^2-1) and not IsSquarefree(n^2+1)]; // _Vincenzo Librandi_, Oct 26 2016

%Y Cf. A002522, A005563, A013929.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Mar 02 2003