A070525 - OEIS

%I #24 Nov 18 2022 10:14:08

%S 2,3,4,6,7,8,12,18,21,30,45,48,70,120,127,153,182,204,212,282,318,322,

%T 910,1167,1177,1342,1680,1963,2670,4398,4655,8088,8599,8808,19680

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

%C 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

%C 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

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A070525.py">A070525.py</a>.

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

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

%o (PARI) isok(n) = isprime(polcyclo(n, eulerphi(n))); \\ _Michel Marcus_, Sep 01 2019

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

%Y Cf. A088856, A090159.

%K nonn,more

%O 1,1

%A _Labos Elemer_, May 02 2002

%E More terms from _T. D. Noe_, Nov 23 2003

%E a(35) by _Lucas A. Brown_, Jan 08 2021