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A055513 Class number h = h- * h+ of cyclotomic field Q( exp(2 Pi / prime(n)) ). 7
1, 1, 1, 1, 1, 1, 1, 3, 8, 9, 37, 121, 211, 695, 4889, 41241, 76301, 853513, 3882809, 11957417, 100146415, 838216959, 13379363737, 411322824001, 3547404378125, 9069094643165, 63434933542623, 161784800122409, 1612072001362952, 2604529186263992195, 28496379729272136525, 646901570175200968153, 1753848916484925681747, 687887859687174720123201, 2333546653547742584439257, 56234327700401832767069245, 10834138978768308207500526544 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,8

COMMENTS

Washington gives a very extensive table (but beware errors!).

REFERENCES

Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, p. 429.

M. Newman, A table of the first factor for prime cyclotomic fields, Math. Comp., 24 (1970), 215-219.

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

LINKS

Table of n, a(n) for n=2..38.

Hisanori Mishima, Factorizations of Cyclotomic Numbers

M. A. Shokrollahi, Tables

EXAMPLE

For n = 9, prime(9) = 23, a(9) = 3.

For n = 38, prime(38) = 163, a(38) = 4*2708534744692077051875131636 = 10834138978768308207500526544.

CROSSREFS

For the relative class number h-, see A000927, which agrees for the first 36 terms, assuming the Generalized Riemann Hypothesis.

Cf. A035115, A055514, A061653.

Sequence in context: A101720 A093439 A000927 * A038226 A095866 A067569

Adjacent sequences:  A055510 A055511 A055512 * A055514 A055515 A055516

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Jun 16 2001

EXTENSIONS

Washington incorrectly gives a(17) = 41421, a(25) = 411322842001.

Edited by Max Alekseyev, Oct 25 2012

STATUS

approved

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Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.