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A061574 Simple quadratic fields (i.e., with a unique prime factorization). 4


%S -163,-67,-43,-19,-11,-7,-3,-2,-1,1,2,3,5,6,7,11,13,14,17,19,21,22,23,

%T 29,31,33,37,38,41,43,46,47,53,57,59,61,62,67,69,71,73,77,83,86,89,93,

%U 94,97,101,103,107,109,113,118,127,129,131,133,134,137,139,141,149

%N Simple quadratic fields (i.e., with a unique prime factorization).

%C -9 <= m < 0: a(m)= -A003173(-m); a(0) = 1; n > 0: a(n) = A003172(n).

%C 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. - _Alonso del Arte_, Feb 10 2011

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, ch. 14.

%H Daniel Forgues (copying T. D. Noe's b003172.txt), <a href="/A061574/b061574.txt">Table of n, a(n) for n = -9..1000</a>

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%t Select[Range[-200, 200], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] == 1 &] (* _T. D. Noe_, Feb 10 2011 *)

%Y Union of A003173 and A003172. Some subsequences: A048981 (requires the fields to be Euclidean), A003174, A003172, see also A003173.

%K sign

%O -9,1

%A _Frank Ellermann_, May 17 2001

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Last modified April 22 16:00 EDT 2021. Contains 343177 sequences. (Running on oeis4.)