A253851 Mersenne primes (A000668) of the form 2^sigma(n) - 1 for some n.

7, 127, 8191, 2147483647, 170141183460469231731687303715884105727

Offset: 1

Author

Jaroslav Krizek, Jan 16 2015

Keywords

• nonn

Comments

Numbers n such that 2^sigma(n) - 1 is a Mersenne primes are given in A253849.

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).

If a(6) exists, it must be bigger than A000668(43) = 2^30402457-1.

Examples

			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.
		

Crossrefs

Cf. A000043, A000203, A000668, A023195, A253849, A253850.

Programs

Magma

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