|
| |
|
|
A000927
|
|
Let p = n-th odd prime; a(n) = "first factor" (or relative class number) h- for cyclotomic field Q( exp(2 P i / p) ).
(Formerly M2711 N1088)
|
|
2
| |
|
|
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, 2708534744692077051875131636
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 3,8
|
|
|
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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
L. C. Washington, Introduction to Cyclotomic Fields, Springer, pp. 353-360.
|
|
|
LINKS
| Hisanori Mishima, Factorizations of Cyclotomic Numbers
M. A. Shokrollahi, Tables
|
|
|
EXAMPLE
| For n = 8, p = 23, a(8) = 3. For n = 37, p = 163, a(37) = 2708534744692077051875131636.
|
|
|
CROSSREFS
| For the full class number h = h- * h+, see A055513, which agrees for the first 36 terms, assuming the Generalized Riemann Hypothesis.
Sequence in context: A025615 A101720 A093439 * A055513 A038226 A095866
Adjacent sequences: A000924 A000925 A000926 * A000928 A000929 A000930
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Washington incorrectly gives a(16) = 41421, a(24) = 411322842001.
|
| |
|
|
