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A247219 Positive numbers n such that n^2 - 1 divides 2^n - 1. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Contains all numbers of the form n = 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 *)

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 A000216

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

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Last modified April 23 03:51 EDT 2021. Contains 343199 sequences. (Running on oeis4.)