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A003172 Q(sqrt n) is a unique factorization domain (or simple quadratic field).
(Formerly M0618)
14
2, 3, 5, 6, 7, 11, 13, 14, 17, 19, 21, 22, 23, 29, 31, 33, 37, 38, 41, 43, 46, 47, 53, 57, 59, 61, 62, 67, 69, 71, 73, 77, 83, 86, 89, 93, 94, 97, 101, 103, 107, 109, 113, 118, 127, 129, 131, 133, 134, 137, 139, 141, 149, 151, 157, 158, 161, 163, 166, 167, 173, 177, 179, 181, 191, 193, 197, 199, 201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Squarefree numbers n such that A003649 is 1. - T. D. Noe, Apr 02 2008

REFERENCES

Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 422-423.

E. L. Ince, Cycles of Reduced Ideals in Quadratic Fields. British Association Mathematical Tables, Vol. 4, London, 1934. (See p. 1.)

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

H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 296.

R. G. Underwood, On the Content Bound for Real Quadratic Field Extensions, Axioms 2013, 2, 1-9; doi:10.3390/axioms2010001. - From N. J. A. Sloane, Feb 03 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for sequences related to quadratic fields

PROG

(PARI)

A007947(n)={my(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i]); }

{ for (n=2, 10^3,

    if ( n!=A007947(n), next() );

    K = bnfinit(x^2 - n);

    if ( K.cyc == [], print1( n, ", ") );

); }

/* Joerg Arndt, Oct 18 2012 */

CROSSREFS

Cf. A061574 (includes negative n), A029702-A029705, A218038-A218042.

Sequence in context: A134669 A053328 A089633 * A053329 A098962 A073485

Adjacent sequences:  A003169 A003170 A003171 * A003173 A003174 A003175

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

The table in Borevich and Shafarevich extends to 497.

STATUS

approved

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Last modified July 25 00:22 EDT 2014. Contains 244897 sequences.