A268130 Primes p of the form sigma(2^k + 1) - 1 for some k >= 0.

2, 3, 5, 17, 47, 83, 257, 1301, 65537, 174767, 5048231, 51322664447, 188313058624991, 4768522825659911, 3148244377723715041631, 211635519858089932125000235391, 906780938207203620571208267879698943, 6392739029893008727817055462596999999

Offset: 1

Author

Jaroslav Krizek, Jan 26 2016

Keywords

• nonn

Comments

Corresponding values of k: 0, 1, 2, 4, 5, 6, 8, 10, 16, 17, 22, 35, 47, 52, 71, 97, 119, 122, 124, 190, 300, ...

Fermat primes from A019434 are in the sequence.

Examples

			Prime 47 is a term because for k = 5, sigma(2^5+1) - 1 = sigma(33) - 1 = 47.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..21

Crossrefs

Cf. A000051, A000203, A069061, A019434.

Programs

Magma

Set(Sort([SumOfDivisors(2^n+1)-1: n in [0..300] | IsPrime(SumOfDivisors(2^n+1)-1)]));

PARI

lista(nn) = for (n=0, nn, if (isprime(p=sigma(2^n + 1) - 1), print1(p, ", "))); \\ Michel Marcus, Jan 27 2016