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

1, 22, 31, 64, 79, 91, 106, 111, 148, 151, 190, 205, 211, 232, 235, 271, 274, 311, 316, 331, 341, 358, 391, 400, 442, 451, 466, 484, 511, 526, 547, 551, 568, 571, 610, 613, 631, 652, 658, 667, 691, 694, 703, 736, 751, 760, 771, 778, 811, 820, 859, 862, 871, 904

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 22 2011

Keywords

• nonn
• hard

Comments

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

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

31=16^2-15^2,

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

79=40^2-39^2,

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

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

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

151=76^2-75^2,

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

211=106^2-105^2.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..62
• David A. Corneth, More terms (this file might miss terms below 10^5, but listed terms are definetely terms)

Crossrefs

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

Programs

Mathematica

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

PARI

isok(n) = !issquarefree(2^n-2) && !issquarefree(2^n+2); \\ Michel Marcus, Oct 04 2019

Extensions

a(14)-a(30) from D. S. McNeil, Mar 23 2011

a(31)-a(54) from Amiram Eldar, Oct 04 2019