

A061653


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


6



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)
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 A016565
Adjacent sequences: A061650 A061651 A061652 * A061654 A061655 A061656


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane, Jun 16 2001


EXTENSIONS

Washington gives an extensive table on pp. 353360.
Missing term a(1) = 1 inserted by N. J. A. Sloane, Feb 05 2009 at the suggestion of Tanya Khovanova
More terms from R. J. Mathar, Feb 06 2009
a(59) changed from 41421 to 41241 (given correctly in 2nd edition of Washington), Matthew Johnson, Jul 20 2013
a(59) in bfile changed as above by Andrew Howroyd, Feb 23 2018
a(97) corrected, a(163) added by Max Alekseyev, Mar 05 2018


STATUS

approved



