A179282 - OEIS

%I #32 Oct 04 2019 08:23:01

%S 1,22,31,64,79,91,106,111,148,151,190,205,211,232,235,271,274,311,316,

%T 331,341,358,391,400,442,451,466,484,511,526,547,551,568,571,610,613,

%U 631,652,658,667,691,694,703,736,751,760,771,778,811,820,859,862,871,904

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

%C Most (not all) of the terms are of the form:

%C x^2-y^2, for x>y>0.

%C 31=16^2-15^2,

%C 64=10^2-6^2=17^2-15^2,

%C 79=40^2-39^2,

%C 91=10^2-3^2=46^2-45^2,

%C 111=20^2-17^2=56^2-55^2,

%C 148=11^2-3^3=38^2-36^2,

%C 151=76^2-75^2,

%C 205=23^2-18^2=103^2-102^2,

%C 211=106^2-105^2.

%H Amiram Eldar, <a href="/A179282/b179282.txt">Table of n, a(n) for n = 1..62</a>

%H 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 2^22-2=2*7^2*127*337, 2^22+2=2*3^2*43*5419.

%t Select[Range@211,!(SquareFreeQ[2^#-2]||SquareFreeQ[2^#+2])&]

%o (PARI) isok(n) = !issquarefree(2^n-2) && !issquarefree(2^n+2); \\ _Michel Marcus_, Oct 04 2019

%Y Cf. A005117, A000918 (2^n-2), A052548 (2^n+2).

%K nonn,hard

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Mar 22 2011

%E a(14)-a(30) from _D. S. McNeil_, Mar 23 2011

%E a(31)-a(54) from _Amiram Eldar_, Oct 04 2019