A247823 Mersenne primes p such that there is a number k with sigma(sigma(2k-1)) = p.

7, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111

Offset: 1

Author

Jaroslav Krizek, Sep 28 2014

Keywords

• nonn
• more

Comments

Mersenne primes p such that there is a number m such that sigma(sigma(m)) = p.

Distinct values attained by the A247822(n) function, in ascending order.

Mersenne primes p such that there are a numbers n and m such that sigma(sigma(2n-1)) = sigma(sigma(2*A247821(n)-1)) = A000203(A000203(2*A247821(n)-1)) = A051027(2*A247821(n)-1) = sigma(sigma(A247838(m))) = A000203(A000203(A247838(m))) = A051027(A247838(m)) where m = 2n-1.

The Mersenne prime 7 is the only prime p such that there is a prime q with sigma(sigma(q)) = p.

Examples

			Mersenne prime 8191 is in sequence because there are numbers n = 1334 and 1969 with sigma(sigma(2*n-1)) = 8191.
		

Crossrefs

Cf. A000203, A008438, A247790, A247791, A247820, A247821, A247822, A247954.

Cf. A000668 (Mersenne primes).

Programs

Magma

Set(Sort([SumOfDivisors(SumOfDivisors(n)): n in [1..10000000] | IsPrime(SumOfDivisors(SumOfDivisors(n)))])) // Jaroslav Krizek, Mar 25 2015

Extensions

a(5)-a(7) from Jaroslav Krizek, Mar 25 2015