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%I #31 Sep 28 2024 14:27:04
%S 2,3,5,17,47,83,257,1301,65537,174767,5048231,51322664447,
%T 188313058624991,4768522825659911,3148244377723715041631,
%U 211635519858089932125000235391,906780938207203620571208267879698943,6392739029893008727817055462596999999
%N Primes p of the form sigma(2^k + 1) - 1 for some k >= 0.
%C 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, ...
%C Fermat primes from A019434 are in the sequence.
%H Jaroslav Krizek, <a href="/A268130/b268130.txt">Table of n, a(n) for n = 1..21</a>
%e Prime 47 is a term because for k = 5, sigma(2^5+1) - 1 = sigma(33) - 1 = 47.
%o (Magma) Set(Sort([SumOfDivisors(2^n+1)-1: n in [0..300] | IsPrime(SumOfDivisors(2^n+1)-1)]));
%o (PARI) lista(nn) = for (n=0, nn, if (isprime(p=sigma(2^n + 1) - 1), print1(p, ", "))); \\ _Michel Marcus_, Jan 27 2016
%Y Cf. A000051, A000203, A069061, A019434.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Jan 26 2016