

A268641


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


1



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
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OFFSET

1,1


COMMENTS

All the listed terms are even squarefree numbers.
Subsequence of A039956.


LINKS

Table of n, a(n) for n=1..56.


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^21]), [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^21) ];


CROSSREFS

Cf. A005117, A007675, A039956, A049532, A049533, A069987, A173186.
Sequence in context: A080766 A262506 A228649 * A162796 A172304 A160164
Adjacent sequences: A268638 A268639 A268640 * A268642 A268643 A268644


KEYWORD

nonn


AUTHOR

K. D. Bajpai, Feb 09 2016


STATUS

approved



