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A046006 Discriminants of imaginary quadratic fields with class number 9 (negated).

%I A046006 #38 Feb 16 2025 08:32:38
%S A046006 199,367,419,491,563,823,1087,1187,1291,1423,1579,2003,2803,3163,3259,
%T A046006 3307,3547,3643,4027,4243,4363,4483,4723,4987,5443,6043,6427,6763,
%U A046006 6883,7723,8563,8803,9067,10627
%N A046006 Discriminants of imaginary quadratic fields with class number 9 (negated).
%C A046006 The class group of Q[sqrt(-4027)] is isomorphic to C_3 X C_3. For all other d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_9. - _Jianing Song_, Dec 01 2019
%H A046006 Steven Arno, M. L. Robinson, Ferrell S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arith. 83 (1998) 295-330.
%H A046006 Duncan A. Buell, <a href="https://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 A046006 Keith Matthews, <a href="http://www.numbertheory.org/classnos/">Tables of imaginary quadratic fields with small class numbers</a>
%H A046006 C. Wagner, <a href="https://dx.doi.org/10.1090/S0025-5718-96-00722-3">Class Number 5, 6 and 7</a>, Math. Comput. 65, 785-800, 1996.
%H A046006 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>
%H A046006 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A046006 Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[10700], NumberFieldClassNumber[Sqrt[-#]] == 9 &]] (* _Jean-François Alcover_, Jun 27 2012 *)
%o A046006 (PARI)
%o A046006 ok(n)={isfundamental(-n) && quadclassunit(-n).no == 9};
%o A046006 for(n=1, 11000, if(ok(n)==1, print1(n, ", "))) \\ _G. C. Greubel_, Mar 01 2019
%o A046006 (Sage)
%o A046006 [n for n in (1..4000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==9] # _G. C. Greubel_, Mar 01 2019
%Y A046006 Cf. A006203, A013658, A014602, A014603, A046002-A046020.
%Y A046006 Cf. A191410.
%K A046006 nonn,fini,full
%O A046006 1,1
%A A046006 _Eric W. Weisstein_