A396479 Numbers k such that psi(k) does not have primitive roots (i.e., is in A033949), where psi = A002322.

13, 17, 25, 26, 29, 31, 32, 34, 35, 37, 39, 41, 43, 45, 49, 50, 51, 52, 53, 55, 58, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 75, 77, 78, 79, 82, 85, 86, 87, 89, 90, 91, 93, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 115, 116, 117, 119

Offset

1,1

Comments

Any rational prime p coprime to N decomposes into a product of EulerPhi(N)/ord(p,N) prime ideals in Z[zeta_N], where ord(p,N) is the multiplicative order of p modulo N. As a result, this sequence lists k such that: there exist some Dirichlet characters chi modulo k such that no rational primes p remain prime in Z[chi], where Z[chi] is the ring generated by values of chi.

Links

Table of n, a(n) for n=1..64.

Wikipedia, Dirichlet character.

Example

13 is a term since there are Dirichlet characters modulo 13 of order 12, and no rational primes remain inert in Z[zeta_12].
32 is a term since there are Dirichlet characters modulo 32 of order 8, and no rational primes remain inert in Z[zeta_8].

Prog

(PARI) isoddprimepower(n) = (n%2) && isprimepower(n)
isA396479(n) = (240%n!=0) && !isoddprimepower(znstar(n)[2][1]/2)

Crossrefs

Cf. A002322, A033949, A061345 (powers of odd primes), A396478 (complement), A396481 (prime terms).

Sequence in context: A145483 A349978 A125262 * A163754 A104278 A129070

Adjacent sequences: A396476 A396477 A396478 * A396480 A396481 A396482

Keyword

nonn,easy

Author

Jianing Song, May 27 2026

Status

approved