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Primes p such that p = 2*phi(sigma((p-1)/2))+ 1.
1

%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