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Mersenne exponents (A000043) that are the sum of the divisors (A000203) of some n.
4

%I #12 Sep 08 2022 08:46:11

%S 3,7,13,31,127

%N Mersenne exponents (A000043) that are the sum of the divisors (A000203) of some n.

%C Also primes p that are the sum of the divisors of some n where 2^sigma(n) - 1 is a Mersenne prime (A000668).

%C Intersection of A023195 and A000043.

%C If a(6) exists, it must be bigger than A000043(43) = 30402457.

%e Mersenne exponent 7 is in the sequence because sigma(4) = 7.

%e Mersenne exponent 31 is in the sequence because there are two numbers n (16 and 25) with sigma(n) = 31.

%o (Magma) Set(Sort([SumOfDivisors(n): n in[1..10000] | IsPrime((2^SumOfDivisors(n))- 1)]))

%Y Cf. A000043, A000203, A000668, A023195, A253849, A253851.

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Jan 16 2015