A396477 Numbers k such that Q(zeta_{psi(k)}) has class number greater than 1, where psi = A002322.

47, 53, 59, 73, 79, 83, 89, 94, 97, 101, 103, 106, 107, 109, 113, 118, 121, 125, 127, 131, 137, 139, 141, 146, 149, 151, 157, 158, 159, 163, 166, 167, 169, 173, 177, 178, 179, 181, 187, 188, 191, 193, 194, 197, 199, 202, 206, 211, 212, 214, 218, 219, 223, 226, 227, 229, 233, 235, 236, 237, 239

Offset

1,1

Comments

In other words, numbers k such that psi(k) > 2 is not in A193175.

Numbers k such that Q(chi) has class number greater than 1 for some Dirichlet characters modulo k, where Q(chi) is the field generated by values of chi.

Contains all but 3100 numbers; see A396476.

Links

Table of n, a(n) for n=1..61.

Wikipedia, Dirichlet character.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Example

47 is a term since there are Dirichlet characters modulo 47 of order 23 or 46, and Q(zeta_23) = Q(zeta_46) does not have class number 1.
73 is a term since there are Dirichlet characters modulo 73 of order 72, and Q(zeta_72) does not have class number 1.

Prog

(PARI) isA396477(n) = (vecsearch([1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 48, 50, 54, 60, 66, 70, 84, 90], A002322(n)) == 0) \\ See A002322 for its program

Crossrefs

Cf. A002322, A193175, A396476 (complement).

Sequence in context: A084366 A257785 A234023 * A128940 A243431 A141279

Adjacent sequences: A396474 A396475 A396476 * A396478 A396479 A396480

Keyword

nonn,easy

Author

Jianing Song, May 27 2026

Status

approved