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Mersenne primes p such that there is a number k with sigma(sigma(2k-1)) = p.
5

%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