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A005848 Cyclotomic fields with class number 1 (or with unique factorization).
(Formerly M2304)
2
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, 44, 45, 48, 60, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

REFERENCES

F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 85, 1983.

J. M. Masley, Where are the number fields with small class number?, pp. 221-242 of Number Theory Carbondale 1979, Lect. Notes Math. 751 (1982).

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 259.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Alf van der Poorten, Notes on Fermat's Last Theorem, Wiley, 1996, p. 14.

L. C. Washington, Introduction to Cyclotomic Fields, Springer, p. 353.

LINKS

Table of n, a(n) for n=1..30.

M. Baake and U. Grimm, A note on shelling

E. Bugarin, M. de las Peñas, D. Frettlöh, Perfect colourings of cyclotomic integers (2009).

J. M. Masley and Hugh L. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256.

CROSSREFS

Cf. A061653.

Sequence in context: A122906 A042965 A260003 * A187885 A039065 A247786

Adjacent sequences:  A005845 A005846 A005847 * A005849 A005850 A005851

KEYWORD

fini,nonn,full,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 23 12:12 EDT 2017. Contains 283952 sequences.