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A176308 Integers n such that n and n^3+-1 are squarefree numbers. 2
6, 42, 66, 78, 102, 114, 138, 186, 210, 222, 258, 282, 318, 330, 354, 366, 390, 402, 438, 462, 498, 510, 534, 546, 642, 678, 690, 714, 762, 786, 798, 858, 870, 894, 906, 942, 966, 978, 1002, 1038, 1086, 1110, 1122, 1218, 1230, 1254, 1266, 1290, 1302, 1338 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All the terms are divisible by 6 since if n == 1, 2, 4, or 5 (mod 6) then either n^3 - 1 or n^3 + 1 is divisible by 9, and if n == 3 (mod 6) then either n^3 - 1 or n^3 + 1 is divisible by 4. - Amiram Eldar, Oct 01 2019

LINKS

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

EXAMPLE

6=2*3; 6^3-1=5*41; 6^3+1=7*31,..

MATHEMATICA

f[n_]:=SquareFreeQ[n]; lst={}; Do[If[f[n^3-1]&&f[n^3+1]&&f[n], AppendTo[lst, n]], {n, 3*6!}]; lst

PROG

(MAGMA) [k:k in [2..1400]| IsSquarefree(k) and IsSquarefree(k^3-1) and IsSquarefree(k^3+1)]; // Marius A. Burtea, Oct 01 2019

CROSSREFS

Cf. A005117.

Sequence in context: A292316 A329000 A329339 * A103763 A191764 A043896

Adjacent sequences:  A176305 A176306 A176307 * A176309 A176310 A176311

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 14 2010

STATUS

approved

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Last modified June 6 13:31 EDT 2020. Contains 334827 sequences. (Running on oeis4.)