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A179282
Numbers n such that 2^n-2 and 2^n+2 are not squarefree.
1
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
1,2
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.
EXAMPLE
2^22-2=2*7^2*127*337, 2^22+2=2*3^2*43*5419.
MATHEMATICA
Select[Range@211, !(SquareFreeQ[2^#-2]||SquareFreeQ[2^#+2])&]
PROG
(PARI) isok(n) = !issquarefree(2^n-2) && !issquarefree(2^n+2); \\ Michel Marcus, Oct 04 2019
CROSSREFS
Cf. A005117, A000918 (2^n-2), A052548 (2^n+2).
Sequence in context: A092215 A239431 A335348 * A106555 A106557 A142347
KEYWORD
nonn,hard
AUTHOR
EXTENSIONS
a(14)-a(30) from D. S. McNeil, Mar 23 2011
a(31)-a(54) from Amiram Eldar, Oct 04 2019
STATUS
approved