A247219 Positive numbers m such that m^2 - 1 divides 2^m - 1.

2, 4, 16, 36, 256, 456, 1296, 2556, 4356, 6480, 8008, 11952, 26320, 44100, 47520, 47880, 49680, 57240, 65536, 74448, 84420, 97812, 141156, 157080, 165600, 225456, 278496, 310590, 333432, 365940, 403900, 419710, 476736, 557040, 560736, 576720, 647088, 1011960, 1033056, 1204560, 1206180

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 26 2014

Keywords

• nonn

Comments

Contains all numbers of the form m = A001146(k) = 2^2^k, k >= 0; and those with k > 1 seem to form the intersection with A247165. - M. F. Hasler, Jul 25 2015

Examples

			2 is in this sequence because 2^2 - 1 = 3 divides 2^2 - 1 = 3.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..105

Crossrefs

Cf. A081762.

Programs

Magma

[n: n in [2..122222] | Denominator((2^n - 1)/(n^2 - 1)) eq 1];

Mathematica

Select[Range[10^4], Divisible[2^# - 1, #^2 - 1] &] (* Alonso del Arte, Nov 26 2014 *)
Select[Range[2,121*10^4],PowerMod[2,#,#^2-1]==1&] (* Harvey P. Dale, Sep 08 2021 *)

PARI

isok(n) = ((2^n - 1) % (n^2 - 1)) == 0; \\ Michel Marcus, Nov 26 2014

PARI

forstep(n=0,1e8,2, Mod(2,n^2-1)^n-1 || print1(n", ")) \\ M. F. Hasler, Jul 25 2015

Python

from gmpy2 import powmod
A247219_list = [n for n in range(2,10**7) if powmod(2,n,n*n-1) == 1]
# Chai Wah Wu, Dec 03 2014

Extensions

Corrected a(24) by Chai Wah Wu, Dec 03 2014