%I #15 Sep 08 2022 08:46:09
%S 7,8191,131071,524287,2147483647,2305843009213693951,
%T 618970019642690137449562111
%N Mersenne primes p such that there is a number k with sigma(sigma(2k-1)) = p.
%C Mersenne primes p such that there is a number m such that sigma(sigma(m)) = p.
%C Distinct values attained by the A247822(n) function, in ascending order.
%C 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.
%C The Mersenne prime 7 is the only prime p such that there is a prime q with sigma(sigma(q)) = p.
%e Mersenne prime 8191 is in sequence because there are numbers n = 1334 and 1969 with sigma(sigma(2*n-1)) = 8191.
%o (Magma) Set(Sort([SumOfDivisors(SumOfDivisors(n)): n in [1..10000000] | IsPrime(SumOfDivisors(SumOfDivisors(n)))])) // _Jaroslav Krizek_, Mar 25 2015
%Y Cf. A000203, A008438, A247790, A247791, A247820, A247821, A247822, A247954.
%Y Cf. A000668 (Mersenne primes).
%K nonn,more
%O 1,1
%A _Jaroslav Krizek_, Sep 28 2014
%E a(5)-a(7) from _Jaroslav Krizek_, Mar 25 2015