A070525 Numbers n such that n-th cyclotomic polynomial evaluated at phi(n) is a prime number.

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

Offset: 1

Author

Labos Elemer, May 02 2002

Keywords

• nonn
• more

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

Examples

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

Links

• Lucas A. Brown, A070525.py.

Crossrefs

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

Cf. A088856, A090159.

Programs

Mathematica

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

PARI

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

Extensions

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

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