Search: id:A000927
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%I A000927 M2711 N1088
%S A000927 1,1,1,1,1,1,1,3,8,9,37,121,211,695,4889,41241,76301,853513,3882809,11957417,
%T A000927 100146415,838216959,13379363737,411322824001,3547404378125,
%U A000927 9069094643165,63434933542623,161784800122409,1612072001362952,2604529186263992195,
               28496379729272136525,646901570175200968153,1753848916484925681747,
               687887859687174720123201,2333546653547742584439257,56234327700401832767069245,
               2708534744692077051875131636
%N 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) ).
%C A000927 Washington gives a very extensive table (but beware errors!).
%D A000927 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000927 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000927 Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, 
               NY, 1966, p. 429.
%D A000927 M. Newman, A table of the first factor for prime cyclotomic fields, Math. 
               Comp., 24 (1970), 215-219.
%D A000927 L. C. Washington, Introduction to Cyclotomic Fields, Springer, pp. 353-360.
%H A000927 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/cn/index.htm">
               Factorizations of Cyclotomic Numbers</a>
%H A000927 M. A. Shokrollahi, <a href="http://www.shokrollahi.com/amin/TAB.html">
               Tables</a>
%e A000927 For n = 8, p = 23, a(8) = 3. For n = 37, p = 163, a(37) = 2708534744692077051875131636.
%Y A000927 For the full class number h = h- * h+, see A055513, which agrees for 
               the first 36 terms, assuming the Generalized Riemann Hypothesis.
%Y A000927 Sequence in context: A025615 A101720 A093439 this_sequence A055513 A038226 
               A095866
%Y A000927 Adjacent sequences: A000924 A000925 A000926 this_sequence A000928 A000929 
               A000930
%K A000927 nonn,nice
%O A000927 3,8
%A A000927 N. J. A. Sloane (njas(AT)research.att.com).
%E A000927 Washington incorrectly gives a(16) = 41421, a(24) = 411322842001.

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