A061494 Relative class number h- of cyclotomic field Q(zeta_n) where n runs through positive integers not congruent to 2 (mod 4) [A042965, but omitting the initial 0].

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 8, 9, 1, 1, 1, 1, 37, 2, 1, 121, 211, 1, 1, 695, 1, 43, 5, 3, 4889, 10, 2, 9, 41241, 1, 76301, 7, 17, 64, 853513, 8, 69, 3882809, 3, 11957417, 11, 19, 1280, 100146415, 5, 2593, 838216959, 1, 6205, 1536, 55, 13379363737, 53872

Offset

1,17

Comments

First edition of Washington incorrectly gives a(44) = h-(Q(zeta_59)) = 41421. [Matthew Johnson, Jul 20 2013]

References

L. C. Washington, Introduction to Cyclotomic Fields, Springer, pp. 353-360.

Links

Table of n, a(n) for n=1..68.

Formula

a(n) = A061653(A042965(n+1)). - M. F. Hasler, Feb 04 2009

Example

n=17: the 17th number not == 2 mod 4 is 23, and Q(zeta_23) = 3 is the first time that h- is bigger than 1, so a(17) = 3.

Crossrefs

Cf. A035115, A055513, A061653, A042965.

Sequence in context: A054724 A360440 A349350 * A360161 A141901 A200473

Adjacent sequences: A061491 A061492 A061493 * A061495 A061496 A061497

Keyword

nonn,nice

Author

N. J. A. Sloane, Jun 16 2001

Extensions

Missing term a(1) = 1 inserted by N. J. A. Sloane, Feb 05 2009 at the suggestion of Tanya Khovanova and M. F. Hasler

More terms (from b-file of A061653), Joerg Arndt, Oct 07 2012

a(44) corrected by Matthew Johnson, Jul 20 2013

Status

approved