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A179282 Numbers n such that 2^n-2 and 2^n+2 are not squarefree.

%I A179282 #32 Oct 04 2019 08:23:01
%S A179282 1,22,31,64,79,91,106,111,148,151,190,205,211,232,235,271,274,311,316,
%T A179282 331,341,358,391,400,442,451,466,484,511,526,547,551,568,571,610,613,
%U A179282 631,652,658,667,691,694,703,736,751,760,771,778,811,820,859,862,871,904
%N A179282 Numbers n such that 2^n-2 and 2^n+2 are not squarefree.
%C A179282 Most (not all) of the terms are of the form:
%C A179282 x^2-y^2, for x>y>0.
%C A179282 31=16^2-15^2,
%C A179282 64=10^2-6^2=17^2-15^2,
%C A179282 79=40^2-39^2,
%C A179282 91=10^2-3^2=46^2-45^2,
%C A179282 111=20^2-17^2=56^2-55^2,
%C A179282 148=11^2-3^3=38^2-36^2,
%C A179282 151=76^2-75^2,
%C A179282 205=23^2-18^2=103^2-102^2,
%C A179282 211=106^2-105^2.
%H A179282 Amiram Eldar, <a href="/A179282/b179282.txt">Table of n, a(n) for n = 1..62</a>
%H A179282 David A. Corneth, <a href="/A179282/a179282.gp.txt">More terms (this file might miss terms below 10^5, but listed terms are definetely terms)</a>
%e A179282 2^22-2=2*7^2*127*337, 2^22+2=2*3^2*43*5419.
%t A179282 Select[Range@211,!(SquareFreeQ[2^#-2]||SquareFreeQ[2^#+2])&]
%o A179282 (PARI) isok(n) = !issquarefree(2^n-2) && !issquarefree(2^n+2); \\ _Michel Marcus_, Oct 04 2019
%Y A179282 Cf. A005117, A000918 (2^n-2), A052548 (2^n+2).
%K A179282 nonn,hard
%O A179282 1,2
%A A179282 _Vladimir Joseph Stephan Orlovsky_, Mar 22 2011
%E A179282 a(14)-a(30) from _D. S. McNeil_, Mar 23 2011
%E A179282 a(31)-a(54) from _Amiram Eldar_, Oct 04 2019