%I #23 Sep 08 2022 08:46:13
%S 3,5,17,257,65537,285121,1425601,2380801,100638721,8778792961,
%T 184354652161
%N Primes p such that p = 2*phi(sigma((p-1)/2))+ 1.
%C The first 5 known Fermat primes from A019434 are in sequence.
%e 17 = 2*phi(sigma((17-1)/2)+1 = 2*phi(15)+1 = 2*8+1, so 17 is in the sequence.
%t Select[Prime@ Range@ 1000000, # == 2 EulerPhi[DivisorSigma[1, (# - 1)/2]] + 1 &] (* _Michael De Vlieger_, Sep 25 2015 *)
%o (Magma) [n: n in [3..1000000] | IsPrime(n) and n eq 2 * EulerPhi(SumOfDivisors((n-1) div 2)) + 1]
%o (PARI) forprime(p=3, 1e8, if((2*eulerphi(sigma((p-1)/2)) + 1) == p, print1(p ", "))) \\ _Altug Alkan_, Sep 25 2015
%Y Cf. A019434, A062401.
%K nonn,more
%O 1,1
%A _Jaroslav Krizek_, Sep 24 2015