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A268641 Squarefree numbers k such that k^2 + 1 and k^2 - 1 are also squarefree.

%I A268641 #9 Sep 08 2022 08:46:15
%S A268641 2,6,14,22,30,34,42,58,66,78,86,94,102,106,110,114,130,138,142,158,
%T A268641 166,178,186,194,202,210,214,222,230,238,254,258,266,286,302,310,322,
%U A268641 330,346,354,358,366,390,394,398,402,410,430,434,438,446,454,462,466,470,498
%N A268641 Squarefree numbers k such that k^2 + 1 and k^2 - 1 are also squarefree.
%C A268641 All the listed terms are even squarefree numbers.
%C A268641 Subsequence of A039956.
%H A268641 Amiram Eldar, <a href="/A268641/b268641.txt">Table of n, a(n) for n = 1..10000</a>
%e A268641 a(2) = 6 = 2 * 3: 6^2 + 1 = 37 = 1 * 37; 6^2 - 1 = 35 = 5 * 7; 6, 37, 35 are all squarefree.
%p A268641 select(n -> andmap(issqrfree, [n, n^2+1, n^2-1]), [seq(n, n=2.. 10^3)]);
%t A268641 Select[Range[1000], SquareFreeQ[#] && SquareFreeQ[#^2 + 1] && SquareFreeQ[#^2 - 1] &]
%o A268641 (PARI) for(n=2, 1000, issquarefree(n) & issquarefree(n^2 + 1) & issquarefree(n^2 - 1) & print1(n,", "))
%o A268641 (Magma) [n : n in [1..1000]  |  IsSquarefree(n) and IsSquarefree(n^2+1) and IsSquarefree(n^2-1) ];
%Y A268641 Cf. A005117, A007675, A039956, A049532, A049533, A069987, A173186.
%K A268641 nonn
%O A268641 1,1
%A A268641 _K. D. Bajpai_, Feb 09 2016