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Numbers n such that Product_{d|(n-2)} phi(d) = Product_{d|(n-1)} phi(d) where phi(x) = Euler totient function (A000010).
3

%I #26 Sep 08 2022 08:46:10

%S 3,5,7,17,257,65537,2200696,2619707,6372796,40588487,76466987,

%T 81591196,118018096,206569607,470542487,525644387,726638836,791937616,

%U 971122516,991172807

%N Numbers n such that Product_{d|(n-2)} phi(d) = Product_{d|(n-1)} phi(d) where phi(x) = Euler totient function (A000010).

%C Numbers n such that A029940(n-2) = A029940(n-1).

%C The first 5 known Fermat primes (A019434) are terms of this sequence.

%C Supersequence of A247164 and A247203.

%F a(n) = A248795(n)+2.

%F A029940(a(n)) = a(n)-1 if a(n) = prime.

%e 17 is in the sequence because A029940(15) = A029940(16) = 64.

%o (Magma) [n: n in [3..100000] | (&*[EulerPhi(d): d in Divisors(n-2)]) eq (&*[EulerPhi(d): d in Divisors(n-1)])]

%Y Cf. A000010, A019434, A029940, A247164, A248795.

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Nov 19 2014

%E a(7)-a(9) using A248795 by _Jaroslav Krizek_, Nov 19 2014

%E a(10)-a(20) using A248795 by _Jaroslav Krizek_, Nov 25 2014