A271842 Positive numbers m such that m^2 - 1 divides 4^m - 1.

2, 4, 6, 16, 36, 52, 66, 256, 378, 456, 1296, 1470, 1548, 1800, 2002, 2556, 4356, 6480, 8008, 11952, 23580, 26320, 33930, 36636, 37170, 43290, 44100, 47520, 47880, 49680, 57240, 65536, 74448, 84420, 97812, 101920, 127050, 134946, 139860, 141156, 157080, 164880, 165600, 209220, 225456

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 15 2016

Keywords

• nonn

Examples

			2 is in this sequence because (4^2 - 1)/(2^2 - 1) = 5.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. positive numbers m such that m^2 - 1 divides (2^k)^m - 1:

A247219 (k=1), this sequence (k=2), A242062 (k=3).

Programs

Magma

[0] cat [n: n in [2..240000] | Denominator((4^n-1)/(n^2-1)) eq 1];

Maple

A271842:=n->`if`((4^n-1) mod (n^2-1) = 0, n, NULL): seq(A271842(n), n=2..10^4); # Wesley Ivan Hurt, Apr 18 2016

Mathematica

Select[Range[1, 100], IntegerQ[(4^# - 1)/(#^2 - 1)] &] (* G. C. Greubel, Apr 15 2016 *)

PARI

is(n)=Mod(4,n^2-1)^n==1 \\ Charles R Greathouse IV, Apr 15 2016