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%I M2304 #41 Aug 09 2022 05:51:52
%S 1,3,4,5,7,8,9,11,12,13,15,16,17,19,20,21,24,25,27,28,32,33,35,36,40,
%T 44,45,48,60,84
%N Cyclotomic fields with class number 1 (or with unique factorization).
%C Note that if n == 2 (mod 4) Q(zeta_n) is the same field as Q(zeta_{n/2}), so this sequence omits numbers that are 2 mod 4. - Yuval Dekel, Jun 07 2003
%C Also note that 3 corresponds to Z[omega] (the Eisenstein integers) and 4 corresponds to Z[i] (the Gaussian integers).
%C Alaca & Williams cite Masley & Montgomery, saying the earlier authors "prove that there are precisely 29 distinct cyclotomic fields" with class number 1 (mentioning the n = 2 mod 4 caveat), and then give this sequence without the initial 1. - _Alonso del Arte_, Mar 10 2017
%D Şaban Alaca & Kenneth S. Williams, Introductory Algebraic Number Theory. Cambridge: Cambridge University Press (2004): 343.
%D F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 85, 1983.
%D J. Myron Masley, Where are the number fields with small class number?, pp. 221-242 of Number Theory Carbondale 1979, Lect. Notes Math. 751 (1982).
%D Paulo Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 259.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D Alf van der Poorten, Notes on Fermat's Last Theorem, Wiley, 1996, p. 14.
%D L. C. Washington, Introduction to Cyclotomic Fields, Springer, p. 353.
%H Michael Baake and Uwe Grimm, <a href="https://arxiv.org/abs/math/0203025">A note on shelling</a>, arXiv:math/0203025 [math.MG], 2002-2003.
%H E. Bugarin, M. de las Peñas, and D. Frettlöh, <a href="http://arxiv.org/abs/0905.4048">Perfect colourings of cyclotomic integers</a>, arXiv:0905.4048 [math.GR], 2009-2012.
%H Hendrik W. Lenstra and A. J. van der Poorten, <a href="https://doi.org/10.1007/BF03024378">Euclidean number fields 1</a>, Math. Intelligencer 2 (1979): pp. 6-15.
%H J. Myron Masley and Hugh L. Montgomery, <a href="http://dx.doi.org/10.1515/crll.1976.286-287.248">Cyclotomic fields with unique factorization</a>, Journal für die reine und angewandte Mathematik 286/287 (1976), 248-256.
%Y Cf. A061653.
%K fini,nonn,full,nice
%O 1,2
%A _N. J. A. Sloane_
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