%I #9 Sep 08 2022 08:46:16

%S 3,5,10,17,65537

%N Numbers n such that sigma(n-1) and sigma(phi(n)) are both primes.

%C Numbers n such that A000203(n-1) and A062402(n) are both primes.

%C There are no other terms <= 10^7.

%C Intersection of A270413 and A062514.

%C Prime terms are in A249759.

%C Corresponding values of sigma(n-1): 3, 7, 13, 31, 131071, ...

%C Corresponding values of sigma(phi(n)): 3, 7, 7, 31, 131071, ...

%C Conjecture: union of number 10 and A249759.

%e 10 is in the sequence because sigma(10-1) = sigma(9) = 13 and sigma(phi(10)) = sigma(4) = 7 (both primes).

%t Select[Range[10^6], And[PrimeQ@ DivisorSigma[1, # - 1], PrimeQ@ DivisorSigma[1, EulerPhi@ #]] &] (* _Michael De Vlieger_, Mar 17 2016 *)

%o (Magma) [n: n in [2..100000] | IsPrime(SumOfDivisors(n-1)) and IsPrime(SumOfDivisors(EulerPhi(n)))]

%o (PARI) isok(n) = isprime(sigma(n-1)) && isprime(sigma(eulerphi(n))); \\ _Michel Marcus_, Mar 17 2016

%Y Cf. A000010, A000203, A062514, A249759, A256438, A270413.

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Mar 16 2016