A272062 Positive numbers k such that k^2 - 1 divides 8^k - 1.

2, 4, 8, 10, 16, 22, 36, 40, 64, 96, 100, 196, 210, 256, 280, 316, 456, 560, 820, 1200, 1236, 1296, 1360, 1408, 1600, 1870, 2380, 2556, 3516, 3616, 4096, 4200, 4356, 5656, 6112, 6256, 6480, 8008, 8688, 10192, 10356, 11440, 11952, 12160, 13728, 14950, 16192, 17020, 19432, 21880, 22036

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 19 2016

Keywords

• nonn

Comments

From Robert Israel, Jun 08 2018: (Start)

All terms are even.

Are 2, 8 and 560 the only terms == 2 (mod 6)? There are no others up to 3*10^9. (End)

Examples

			a(1) = 2 because (8^2 - 1)/(2^2 - 1) = 21.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2559

Crossrefs

Cf. positive numbers n such that n^2 - 1 divides (2^k)^n - 1: A247219 (k=1), A271842 (k=2), this sequence (k=3).

Programs

Magma

[0] cat [n: n in [2..30000] | Denominator((8^n-1)/(n^2-1)) eq 1];

Maple

A272062:=n->`if`((8^n-1) mod (n^2-1) = 0, n, NULL): seq(A272062(n), n=2..5*10^4); # Wesley Ivan Hurt, Apr 21 2016

Mathematica

Select[Range[2, 22100], Divisible[8^# - 1, #^2 - 1] &] (* Michael De Vlieger, Apr 19 2016 *)

PARI

is(n)=Mod(8,n^2-1)^n==1 \\ Charles R Greathouse IV, Apr 19 2016