A247219 - OEIS

%I #34 Jun 27 2024 22:21:45

%S 2,4,16,36,256,456,1296,2556,4356,6480,8008,11952,26320,44100,47520,

%T 47880,49680,57240,65536,74448,84420,97812,141156,157080,165600,

%U 225456,278496,310590,333432,365940,403900,419710,476736,557040,560736,576720,647088,1011960,1033056,1204560,1206180

%N Positive numbers m such that m^2 - 1 divides 2^m - 1.

%C 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

%H Chai Wah Wu, <a href="/A247219/b247219.txt">Table of n, a(n) for n = 1..105</a>

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

%t Select[Range[10^4], Divisible[2^# - 1, #^2 - 1] &] (* _Alonso del Arte_, Nov 26 2014 *)

%t Select[Range[2,121*10^4],PowerMod[2,#,#^2-1]==1&] (* _Harvey P. Dale_, Sep 08 2021 *)

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

%o (PARI) isok(n) = ((2^n - 1) % (n^2 - 1)) == 0; \\ _Michel Marcus_, Nov 26 2014

%o (Python)

%o from gmpy2 import powmod

%o A247219_list = [n for n in range(2,10**7) if powmod(2,n,n*n-1) == 1]

%o # _Chai Wah Wu_, Dec 03 2014

%o (PARI) forstep(n=0,1e8,2, Mod(2,n^2-1)^n-1 || print1(n", ")) \\ _M. F. Hasler_, Jul 25 2015

%Y Cf. A081762.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Nov 26 2014

%E Corrected a(24) by _Chai Wah Wu_, Dec 03 2014