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%I #10 Sep 08 2022 08:46:11
%S 7,127,8191,2147483647,170141183460469231731687303715884105727
%N Mersenne primes (A000668) of the form 2^sigma(n) - 1 for some n.
%C Numbers n such that 2^sigma(n) - 1 is a Mersenne primes are given in A253849.
%C Sequence of corresponding values of sigma(n) are given in A253850 and each term of this sequence must be a prime from the sequence of Mersenne exponents (A000043).
%C If a(6) exists, it must be bigger than A000668(43) = 2^30402457-1.
%e Mersenne prime 2147483647 is in the sequence because there are two numbers n (16 and 25) with 2^sigma(n) - 1 = 2^31 - 1 = 2147483647.
%o (Magma) Set(Sort([(2^SumOfDivisors(n))-1: n in[1..10000] | IsPrime((2^SumOfDivisors(n))-1)]))
%Y Cf. A000043, A000203, A000668, A023195, A253849, A253850.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Jan 16 2015
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