A247219 - OEIS

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

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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