

A247791


Primes p such that there is a prime q for which sigma(sigma(2q1)) = p.


5




OFFSET

1,1


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(2q1)) = A247954(q) = A000203(A000203(2q1)) = A000203(A008438(q1)) = A051027(2q1) = 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*5004615538020192611)) where 500461553802019261 is prime (see comment of Hiroaki Yamanouchi in A247821).  Jaroslav Krizek, Oct 08 2014


LINKS

Table of n, a(n) for n=1..3.


EXAMPLE

Prime 7 is in sequence because there is prime 2 such that sigma(sigma(2*21)) = sigma(sigma(3)) = sigma(4) = 7.


PROG

(MAGMA)[SumOfDivisors(SumOfDivisors(2*n1)): n in [A247790(n)]
(MAGMA)[SumOfDivisors(SumOfDivisors(2*n1)): n in[1..1000000]  IsPrime(SumOfDivisors(SumOfDivisors(2*n1))) and IsPrime(n)]
(PARI)
forprime(p=1, 10^7, if(ispseudoprime(sigma(sigma(2*p1))), print1(sigma(sigma(2*p1)), ", "))) \\ Derek Orr, Sep 29 2014


CROSSREFS

Cf. A000203, A008438, A247790, A247820, A247821, A247822, A247823, A247954.
Sequence in context: A291906 A090769 A013842 * A243859 A297059 A306256
Adjacent sequences: A247788 A247789 A247790 * A247792 A247793 A247794


KEYWORD

nonn,more,bref


AUTHOR

Jaroslav Krizek, Sep 28 2014


STATUS

approved



