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A055513
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Class number h = h- * h+ of cyclotomic field Q( exp(2 Pi / prime(n)) ).
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9
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1, 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
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OFFSET
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1,9
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COMMENTS
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Washington gives a very extensive table (but beware errors!).
h+(n) denotes the class number of Q(exp(2*Pi/n) + exp(-2*Pi/n)).
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REFERENCES
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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.
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LINKS
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EXAMPLE
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For n = 9, prime(9) = 23, a(9) = 3.
For n = 38, prime(38) = 163, a(38) = 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. See also A230869 and A230870.
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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Washington incorrectly gives a(17) = 41421, a(25) = 411322842001.
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STATUS
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approved
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