A070524 -id:A070524

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A070525

Numbers n such that n-th cyclotomic polynomial evaluated at phi(n) is a prime number.

+0
3

2, 3, 4, 6, 7, 8, 12, 18, 21, 30, 45, 48, 70, 120, 127, 153, 182, 204, 212, 282, 318, 322, 910, 1167, 1177, 1342, 1680, 1963, 2670, 4398, 4655, 8088, 8599, 8808, 19680

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OFFSET

1,1

COMMENTS

These are probable primes for n > 910. No others for n <= 10000. The prime values of n are 2, 3, 7, 127 and 8599 (A088856). - T. D. Noe, Nov 23 2003

All terms <= 2670, except 1963, have been certified prime with PARI's ECPP. There are no other terms <= 25000. - Lucas A. Brown, Jan 08 2021

LINKS

Table of n, a(n) for n=1..35.

Lucas A. Brown, A070525.py.

EXAMPLE

n=7: Phi(7)=6, Cyclotomic(7,6)=1+6+36+216+1296+7776+46656=55987 is prime.

MATHEMATICA

Do[s=Cyclotomic[n, EulerPhi[n]]; If[PrimeQ[s], Print[n]], {n, 1, 400}]

PROG

(PARI) isok(n) = isprime(polcyclo(n, eulerphi(n))); \\ Michel Marcus, Sep 01 2019

CROSSREFS

Cf. A070518, A070519, A070520, A070521, A070522, A070523, A070524.

Cf. A088856, A090159.

KEYWORD

nonn,more

AUTHOR

Labos Elemer, May 02 2002

EXTENSIONS

More terms from T. D. Noe, Nov 23 2003

a(35) by Lucas A. Brown, Jan 08 2021

STATUS

approved

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