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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). 2
3, 5, 17, 257, 65537, 991172807 (list; graph; refs; listen; history; text; internal format)
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 A263539

Adjacent sequences:  A247200 A247201 A247202 * A247204 A247205 A247206

KEYWORD

nonn,more

AUTHOR

Jaroslav Krizek, Nov 25 2014

STATUS

approved

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Last modified August 22 07:02 EDT 2017. Contains 290943 sequences.