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 A253235 Numbers n such that the n-th cyclotomic polynomial has no root mod p for all primes p <= n. 7
 1, 12, 15, 24, 28, 30, 33, 35, 36, 40, 44, 45, 48, 51, 56, 60, 63, 65, 66, 69, 70, 72, 75, 76, 77, 80, 84, 85, 87, 88, 90, 91, 92, 95, 96, 99, 102, 104, 105, 108, 112, 115, 117, 119, 120, 123, 124, 126, 130, 132, 133, 135, 138, 140, 141, 143, 144, 145, 150, 152, 153, 154 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers n such that A253236(n) = 0. Numbers n such that all divisors of Phi_n(b) are congruent to 1 (mod n) for every natural number b. If p is prime, k, r are natural numbers, then: Every n = p^r is not in this sequence. Every n = 2p^r is not in this sequence. n = 3p^r (p>3) is in this sequence iff p != 1 (mod 3). n = 4p^r (p>4) is in this sequence iff p != 1 (mod 4). n = 5p^r (p>5) is in this sequence iff p != 1 (mod 5). ... n = kp^r (p>k) is in this sequence iff p != 1 (mod k). LINKS Eric Chen and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Chen) PROG (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 CROSSREFS For A253236(n) = 2, 3, 5, 7, 11, 13, see A000079, A038754, A245478, A245479, A245480, A245481. Sequence in context: A122040 A342758 A274550 * A050480 A290508 A063604 Adjacent sequences: A253232 A253233 A253234 * A253236 A253237 A253238 KEYWORD nonn AUTHOR Eric Chen, Apr 19 2015 STATUS approved

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Last modified November 30 18:31 EST 2023. Contains 367461 sequences. (Running on oeis4.)