A061653 - OEIS

A061653

Relative class number h- of cyclotomic field Q(zeta_n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 8, 1, 9, 1, 1, 1, 1, 1, 37, 1, 2, 1, 121, 1, 211, 1, 1, 3, 695, 1, 43, 1, 5, 3, 4889, 1, 10, 2, 9, 8, 41241, 1, 76301, 9, 7, 17, 64, 1, 853513, 8, 69, 1, 3882809, 3, 11957417, 37, 11, 19, 1280, 2, 100146415

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OFFSET

1,23

COMMENTS

Note that if n == 2 (mod 4), Q(zeta_n) is the same field as Q(zeta_{n/2}).

From Richard N. Smith, Jul 15 2019: (Start)

For prime p, p divides a(p) (or a(2p)) if and only if p is in A000928.

For prime p, p divides a(4p) if and only if p is in A250216. (End)

LINKS

Richard N. Smith, Table of n, a(n) for n = 1..256 (terms 1..163 from R. J. Mathar)

Dylan Johnston, Diego Martín Duro, and Dmitriy Rumynin, Disconnected Reductive Groups: Classification and Representations, arXiv:2409.06375 [math.RT], 2024. See p. 14.

L. C. Washington, Introduction to Cyclotomic Fields, Springer, p. 353. [WARNING: The table contains errors for n=59, 97, ...]

FORMULA

For prime p, a(p) = A000927(A000720(p)).

EXAMPLE

Q(zeta_23) = 3 is the first time that h- is bigger than 1.

CROSSREFS

Contains A000927, A035115, A061494 as subsequences.

Cf. A055513, A005848.

Sequence in context: A046535 A324198 A135939 * A069226 A326697 A366168

Adjacent sequences: A061650 A061651 A061652 * A061654 A061655 A061656

KEYWORD

nonn,easy,nice