A247203 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).

3, 5, 17, 257, 65537, 991172807

Offset

1,1

Comments

Primes p such that A000010(p-2) = A000010(p-1) and simultaneously A029940(p-2) = A029940(p-1).

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

Supersequence of A247164 and A248796.

Links

Table of n, a(n) for n=1..6.

Example

17 is in the sequence because phi(15) = phi(16) = 8 and simultaneously Product_{d|15} phi(d) = Product_{d|16} phi(d) = 64.

Prog

(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)]
(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)]

Crossrefs

Cf. A000010, A029940, A247164, A248796.

Sequence in context: A254576 A232720 A272061 * A262534 A000215 A339344

Adjacent sequences: A247200 A247201 A247202 * A247204 A247205 A247206

Keyword

nonn,more

Author

Jaroslav Krizek, Nov 25 2014

Status

approved