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A268641
Squarefree numbers k such that k^2 + 1 and k^2 - 1 are also squarefree.
2
2, 6, 14, 22, 30, 34, 42, 58, 66, 78, 86, 94, 102, 106, 110, 114, 130, 138, 142, 158, 166, 178, 186, 194, 202, 210, 214, 222, 230, 238, 254, 258, 266, 286, 302, 310, 322, 330, 346, 354, 358, 366, 390, 394, 398, 402, 410, 430, 434, 438, 446, 454, 462, 466, 470, 498
OFFSET
1,1
COMMENTS
All the listed terms are even squarefree numbers.
Subsequence of A039956.
LINKS
EXAMPLE
a(2) = 6 = 2 * 3: 6^2 + 1 = 37 = 1 * 37; 6^2 - 1 = 35 = 5 * 7; 6, 37, 35 are all squarefree.
MAPLE
select(n -> andmap(issqrfree, [n, n^2+1, n^2-1]), [seq(n, n=2.. 10^3)]);
MATHEMATICA
Select[Range[1000], SquareFreeQ[#] && SquareFreeQ[#^2 + 1] && SquareFreeQ[#^2 - 1] &]
PROG
(PARI) for(n=2, 1000, issquarefree(n) & issquarefree(n^2 + 1) & issquarefree(n^2 - 1) & print1(n, ", "))
(Magma) [n : n in [1..1000] | IsSquarefree(n) and IsSquarefree(n^2+1) and IsSquarefree(n^2-1) ];
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Feb 09 2016
STATUS
approved