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A046005 Discriminants of imaginary quadratic fields with class number 8 (negated).

%I A046005 #28 Feb 16 2025 08:32:38
%S A046005 95,111,164,183,248,260,264,276,295,299,308,371,376,395,420,452,456,
%T A046005 548,552,564,579,580,583,616,632,651,660,712,820,840,852,868,904,915,
%U A046005 939,952,979,987,995,1032,1043,1060,1092,1128,1131,1155,1195,1204
%N A046005 Discriminants of imaginary quadratic fields with class number 8 (negated).
%C A046005 131 discriminants in this sequence (almost certainly but not proved).
%H A046005 Andrew Howroyd, <a href="/A046005/b046005.txt">Table of n, a(n) for n = 1..131</a>
%H A046005 Steven Arno, M. L. Robinson and Ferrel S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arithm. 83.4 (1998), 295-330
%H A046005 Duncan A. Buell, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796.
%H A046005 C. Wagner, <a href="http://dx.doi.org/10.1090/S0025-5718-96-00722-3">Class Number 5, 6 and 7</a>, Math. Comput. 65, 785-800, 1996.
%H A046005 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>
%H A046005 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A046005 Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[6400], NumberFieldClassNumber[Sqrt[-#]] == 8 &]] (* _Jean-François Alcover_, Jun 27 2012 *)
%o A046005 (PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no == 8} \\ _Andrew Howroyd_, Jul 20 2018
%o A046005 (Sage) [n for n in (1..6500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==8] # _G. C. Greubel_, Mar 01 2019
%Y A046005 Cf. A006203, A013658, A014602, A014603, A046002-A046020, A305416.
%Y A046005 Cf. A191410.
%K A046005 nonn,fini
%O A046005 1,1
%A A046005 _Eric W. Weisstein_