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

1,1

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

Links

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

Example

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

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 *)

Prog

(Magma) [n: n in [2..122222] | Denominator((2^n - 1)/(n^2 - 1)) eq 1];
(PARI) isok(n) = ((2^n - 1) % (n^2 - 1)) == 0; \\ Michel Marcus, Nov 26 2014
(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
(PARI) forstep(n=0, 1e8, 2, Mod(2, n^2-1)^n-1 || print1(n", ")) \\ M. F. Hasler, Jul 25 2015

Crossrefs

Cf. A081762.

Sequence in context: A087965 A074411 A189838 * A265835 A185074 A379525

Adjacent sequences: A247216 A247217 A247218 * A247220 A247221 A247222

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 26 2014

Extensions

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

Status

approved