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Search: id:A055513
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| A055513 |
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Let p = n-th odd prime; a(n) = class number h = h- * h+ of cyclotomic field Q( exp(2 P i / p) ). |
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+0
5
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| 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; listen)
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OFFSET
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1,8
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COMMENT
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Washington gives a very extensive table (but beware errors!).
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REFERENCES
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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.
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LINKS
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Hisanori Mishima, Factorizations of Cyclotomic Numbers
M. A. Shokrollahi, Tables
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EXAMPLE
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For n = 8, p = 23, a(8) = 3. For n = 37, p = 163, a(37) = 4*2708534744692077051875131636 = 10834138978768308207500526544.
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CROSSREFS
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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 this_sequence A038226 A095866 A067569
Adjacent sequences: A055510 A055511 A055512 this_sequence A055514 A055515 A055516
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 16 2001
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EXTENSIONS
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Washington incorrectly gives a(16) = 41421, a(24) = 411322842001.
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