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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.

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

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 May 25 01:01 EDT 2017. Contains 287008 sequences.