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