%I #33 Apr 22 2015 13:18:48
%S 1,12,15,24,28,30,33,35,36,40,44,45,48,51,56,60,63,65,66,69,70,72,75,
%T 76,77,80,84,85,87,88,90,91,92,95,96,99,102,104,105,108,112,115,117,
%U 119,120,123,124,126,130,132,133,135,138,140,141,143,144,145,150,152,153,154
%N Numbers n such that the n-th cyclotomic polynomial has no root mod p for all primes p <= n.
%C Numbers n such that A253236(n) = 0.
%C Numbers n such that all divisors of Phi_n(b) are congruent to 1 (mod n) for every natural number b.
%C If p is prime, k, r are natural numbers, then:
%C Every n = p^r is not in this sequence.
%C Every n = 2p^r is not in this sequence.
%C n = 3p^r (p>3) is in this sequence iff p != 1 (mod 3).
%C n = 4p^r (p>4) is in this sequence iff p != 1 (mod 4).
%C n = 5p^r (p>5) is in this sequence iff p != 1 (mod 5).
%C ...
%C n = kp^r (p>k) is in this sequence iff p != 1 (mod k).
%H Eric Chen and Charles R Greathouse IV, <a href="/A253235/b253235.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Chen)
%o (PARI) is(n)=my(P=polcyclo(n), f=factor(n)[, 1]); for(i=1, #f, if(#polrootsmod(P, f[i]), return(0))); 1 \\ _Charles R Greathouse IV_, Apr 20 2015
%Y For A253236(n) = 2, 3, 5, 7, 11, 13, see A000079, A038754, A245478, A245479, A245480, A245481.
%K nonn
%O 1,2
%A _Eric Chen_, Apr 19 2015