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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 (list; graph; refs; listen; history; text; internal format)
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.
Sequence in context: A046535 A324198 A135939 * A069226 A326697 A366168
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jun 16 2001
EXTENSIONS
Washington gives an extensive table on pp. 353-360.
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 b-file changed as above by Andrew Howroyd, Feb 23 2018
a(97) corrected, a(163) added by Max Alekseyev, Mar 05 2018
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)