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A061574
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Simple quadratic fields (i.e. with a unique prime factorization).
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1
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-163, -67, -43, -19, -11, -7, -3, -2, -1, 1, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| -9,1
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COMMENTS
| -9 <= m < 0: a(m)= -A003173(-m); a(0)= 1; n > 0: a(n)= A003172(n).
Squarefree values of n for which the quadratic field Q[ Sqrt(n) ] is a unique factorization domain, but not necessarily Euclidean. All negative values are listed. [From Alonso del Arte, Feb 10 2011]
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REFERENCES
| G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, ch. 14.
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LINKS
| Index entries for sequences related to quadratic fields
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MATHEMATICA
| Select[Range[-200, 200], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] == 1 &] (* From T. D. Noe, Feb 10 2011 *)
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CROSSREFS
| Union of A003173 and A003172. Some subsequences: A048981 (requires the fields to be Euclidean), A003174, A003172, see also A003173.
Sequence in context: A183812 A036914 A030442 * A185444 A057604 A132250
Adjacent sequences: A061571 A061572 A061573 * A061575 A061576 A061577
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KEYWORD
| sign
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AUTHOR
| Frank Ellermann (Frank.Ellermann(AT)t-online.de), May 17 2001
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