A173186 -id:A173186 - cp's OEIS frontend

A228140 Numbers n such that n^2 - 2 is not squarefree.

10, 39, 45, 58, 59, 88, 108, 116, 137, 156, 157, 186, 206, 235, 244, 255, 284, 304, 333, 334, 338, 353, 373, 382, 402, 414, 431, 451, 477, 480, 500, 529, 533, 549, 578, 598, 623, 627, 647, 665, 676, 685, 696, 717, 725, 745, 774, 794, 822, 823, 843, 845, 872, 892, 902, 912, 921, 941

Offset: 1

Gerasimov Sergey, Aug 12 2013

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A005117, A008865, A013929, A173186.

remove(n -> numtheory:-issqrfree(n^2-2), [$1..1000]); # Robert Israel, Nov 03 2019

Select[Range[1000],!SquareFreeQ[#^2-2]&] (* Harvey P. Dale, Jun 14 2021 *)

{n: A008865(n) in A013929} . - R. J. Mathar, Sep 26 2013

Corrected by R. J. Mathar, Sep 26 2013

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

Original entry on oeis.org

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

K. D. Bajpai, Feb 09 2016

nonn

All the listed terms are even squarefree numbers.

Subsequence of A039956.

			a(2) = 6 = 2 * 3: 6^2 + 1 = 37 = 1 * 37; 6^2 - 1 = 35 = 5 * 7; 6, 37, 35 are all squarefree.

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

Cf. A005117, A007675, A039956, A049532, A049533, A069987, A173186.

[n : n in [1..1000]  |  IsSquarefree(n) and IsSquarefree(n^2+1) and IsSquarefree(n^2-1) ];

select(n -> andmap(issqrfree, [n, n^2+1, n^2-1]), [seq(n, n=2.. 10^3)]);

Select[Range[1000], SquareFreeQ[#] && SquareFreeQ[#^2 + 1] && SquareFreeQ[#^2 - 1] &]

for(n=2, 1000, issquarefree(n) & issquarefree(n^2 + 1) & issquarefree(n^2 - 1) & print1(n,", "))

A088034 Even numbers k such that k^2-1 is divisible by a square > 1.

Original entry on oeis.org

8, 10, 24, 26, 28, 44, 46, 48, 50, 62, 64, 74, 76, 80, 82, 98, 100, 116, 118, 120, 122, 124, 126, 134, 136, 146, 148, 152, 154, 168, 170, 172, 174, 176, 188, 190, 206, 208, 224, 226, 242, 244, 246, 260, 262, 274, 276, 278, 280, 288, 290, 296, 298, 314, 316, 324

Offset: 1

Amarnath Murthy, Sep 19 2003

nonn

Intersection of A005843 and A173186.

Cf. A088033.

Select[Range[2,400,2],!SquareFreeQ[#^2-1]&] (* Harvey P. Dale, Jan 15 2012 *)

More terms from Ray Chandler, Sep 23 2003

Offset changed by Andrew Howroyd, Sep 22 2024

cp's OEIS Frontend

A228140 Numbers n such that n^2 - 2 is not squarefree.

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

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A088034 Even numbers k such that k^2-1 is divisible by a square > 1.

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