OFFSET

1,1

COMMENTS

When n is prime, then the solutions are given in A088790.

No term of this sequence is congruent to 1 mod 4. In general, if k = s^2*t where t is squarefree and t == 1 (mod 4), then Cyclotomic(k,t*x^2) is the product of two polynomials. See the Wikipedia link below. - Jianing Song, Sep 25 2019

All terms <= 1858 have been proven with PARI's implementation of ECPP. All larger terms are BPSW PRPs. There are no further terms <= 30000. - Lucas A. Brown, Dec 28 2020

LINKS

Eric Weisstein's World of Mathematics, Cyclotomic Polynomial

Wikipedia, Aurifeuillean factorization

MATHEMATICA

Do[s=Cyclotomic[n, n]; If[PrimeQ[s], Print[n]], {n, 2, 256}]

PROG

(PARI) for(n=2, 10^9, if(ispseudoprime(polcyclo(n, n)), print1(n, ", "))); \\ Joerg Arndt, Jan 22 2015

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Labos Elemer, May 02 2002

EXTENSIONS

More terms from T. D. Noe, Oct 17 2003

a(29) from Charles R Greathouse IV, May 05 2011

STATUS

approved