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Primes p such that sigma(2^(p+1)) is prime.
1

%I #16 Sep 08 2022 08:46:17

%S 3,5,11,17,29,59,1277,4421,110501,132047,20996009,24036581

%N Primes p such that sigma(2^(p+1)) is prime.

%C Primes in A153798 = A000043 - 2 where A000043 = Mersenne exponents.

%C Corresponding values of primes q are in A278054.

%C See A000043 (Mersenne exponents) - numbers n such that sigma(2^(n-1)) is a prime.

%e Prime 11 is in the sequence because sigma(2^(11+1)) = sigma(4096) = 8191 (prime).

%t (* set the terms in A000043 = lst *) Select[lst, PrimeQ[# - 2] &] (* _Robert G. Wilson v_, Nov 09 2016 *)

%o (Magma) [n: n in [1..10000] | IsPrime(n) and IsPrime(SumOfDivisors(2^(n+1)))]

%o (PARI) is(n)=isprime(n) && isprime(n+2) && isprime(2^(n+2)-1) \\ _Charles R Greathouse IV_, Nov 09 2016

%Y Cf. A000043, A000203, A153798, A278054.

%K hard,nonn,more

%O 1,1

%A _Jaroslav Krizek_, Nov 09 2016