A247791 Primes p such that there is a prime q for which sigma(sigma(2*q-1)) = p.

7, 131071, 524287

Offset: 1

Author

Jaroslav Krizek, Sep 28 2014

Keywords

• nonn
• more
• bref

Comments

The next term, if it exists, must be greater than 5*10^7.

Primes p such that there is prime q for which sigma(sigma(2*q-1)) = A247954(q) = A000203(A000203(2*q-1)) = A000203(A008438(q-1)) = A051027(2*q-1) = p.

Corresponding values of primes q: 2, 28669, 126961, ... (A247790).

Conjecture: Subsequence of Mersenne primes.

Conjecture: the next term is 2305843009213693951 when 2305843009213693951 = sigma(sigma(2*500461553802019261-1)) where 500461553802019261 is prime (see comment of Hiroaki Yamanouchi in A247821). - Jaroslav Krizek, Oct 08 2014

Examples

			Prime 7 is in sequence because there is prime 2 such that sigma(sigma(2*2-1)) = sigma(sigma(3)) = sigma(4) = 7.
		

Crossrefs

Cf. A000203, A008438, A247790, A247820, A247821, A247822, A247823, A247954.

Programs

Magma

[SumOfDivisors(SumOfDivisors(2*n-1)): n in [A247790(n)]];

Magma

[SumOfDivisors(SumOfDivisors(2*n-1)): n in[1..1000000] | IsPrime(SumOfDivisors(SumOfDivisors(2*n-1))) and IsPrime(n)];

PARI

forprime(p=1,10^7,if(ispseudoprime(sigma(sigma(2*p-1))),print1(sigma(sigma(2*p-1)),", "))) \\ Derek Orr, Sep 29 2014