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, 1872619667, 4081364447

Offset: 1

Author

Jaroslav Krizek, Nov 25 2014

Keywords

• nonn
• more

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.

Examples

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

Crossrefs

Subsequence of A247164 and A248796.

Cf. A000010, A029940.

Programs

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)];

Extensions

a(7)-a(8) from Jinyuan Wang, Jul 27 2025