A262978 Exponents n such that 2^n-1 and 2^n+1 are squarefree.

1, 2, 4, 5, 7, 8, 11, 13, 14, 16, 17, 19, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 41, 43, 44, 46, 47, 49, 52, 53, 56, 58, 59, 61, 62, 64, 65, 67, 71, 73, 74, 76, 77, 79, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 101, 103, 104, 106, 107, 109, 112, 113, 115, 116, 118, 119

Offset: 1

Author

Juri-Stepan Gerasimov, May 01 2016

Keywords

• nonn
• easy

Examples

			a(4) = 5 because 2^5 - 1 = 31 and 2^5 + 1 = 33 are squarefree numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..608

Crossrefs

Cf. A000961, A229303, A269758.

Programs

Magma

[n: n in [1..120] | IsSquarefree(2^n-1) and IsSquarefree(2^n+1)];

Mathematica

Select[Range[120],AllTrue[2^#+{1,-1},SquareFreeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 20 2019 *)

PARI

is(n)=issquarefree(2^n-1) && issquarefree(2^n+1) \\ Charles R Greathouse IV, May 02 2016

Formula

2^a(n) = A269758(n).