%I
%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
