A127643 Composite numbers k that divide A123591(k) = ((2^k - 1)^(2^k) - 1)/(2^k)^2.

15, 51, 65, 85, 185, 221, 255, 341, 451, 533, 561, 595, 645, 679, 771, 1059, 1095, 1105, 1271, 1285, 1313, 1387, 1455, 1581, 1729, 1905, 2045, 2047, 2091, 2307, 2465, 2701, 2755, 2821, 2895, 3201, 3205, 3277, 3281, 3341, 3603, 3655, 3723, 3855, 4033, 4039

Offset: 1

Author

Alexander Adamchuk, Jan 22 2007

Keywords

• nonn

Comments

p divides A123591(p) for prime p > 2.

Odd composite numbers k such that (2^k-1)^(2^k) == 1 (mod k). - Robert Israel, Jul 06 2017

Links

• Robert Israel, Table of n, a(n) for n = 1..571

Crossrefs

Cf. A123591, A085606.

Programs

Maple

select(n -> not isprime(n) and (2^n-1) &^ (2^n) mod n = 1, [seq(i,i=9..10000,2)]); # Robert Israel, Jul 06 2017

Mathematica

Do[f=PowerMod[(2^n-1),(2^n),n]-1;If[ !PrimeQ[n]&&IntegerQ[(n+1)/2]&&IntegerQ[f/n],Print[n]],{n,2,10000}]