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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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) ];

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