|
%I #12 Sep 08 2022 08:46:09
%S 3,5,17,257,65537,991172807
%N Primes p such that phi(p-2) = phi(p-1) and simultaneously Product_{d|(p-2)} phi(d) = Product_{d|(p-1)} phi(d) where phi(x) = Euler totient function (A000010).
%C Primes p such that A000010(p-2) = A000010(p-1) and simultaneously A029940(p-2) = A029940(p-1).
%C The first 5 known Fermat primes (A019434) are terms of this sequence.
%C Supersequence of A247164 and A248796.
%e 17 is in the sequence because phi(15) = phi(16) = 8 and simultaneously Product_{d|15} phi(d) = Product_{d|16} phi(d) = 64.
%o (Magma) [p: p in PrimesInInterval(3, 10^7) | (&*[EulerPhi(d): d in Divisors(p-2)]) eq (&*[EulerPhi(d): d in Divisors(p-1)]) and EulerPhi(p-2) eq EulerPhi(p-1)]
%o (Magma) [n: n in [A248796(n)] | IsPrime(n) and EulerPhi(n-2) eq EulerPhi(n-1)] (Magma) [n: n in [A247164(n)] | IsPrime(n) and EulerPhi(n-2) eq EulerPhi(n-1)]
%Y Cf. A000010, A029940, A247164, A248796.
%K nonn,more
%O 1,1
%A _Jaroslav Krizek_, Nov 25 2014
| 