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A351670 Discriminants of imaginary quadratic fields with class number 32 (negated).

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%I A351670 #10 Feb 16 2025 08:34:03
%S A351670 791,1119,1239,1463,1551,1767,1784,1943,2084,2180,2276,2343,2840,2847,
%T A351670 2996,3080,3156,3199,3207,3236,3247,3295,3428,3476,3679,3812,3895,
%U A351670 4088,4296,4340,4495,4584,4647,4767,4868,4884,4964,4980,4996,5012,5064,5192,5215
%N A351670 Discriminants of imaginary quadratic fields with class number 32 (negated).
%C A351670 Sequence contains 708 terms; largest is 164803.
%C A351670 The class groups associated to 187 of the above discriminants are isomorphic to C_32, 273 have a class group isomorphic to C_16 X C_2, 160 isomorphic to C_8 X C_2 X C_2, 60 have a class group isomorphic to C_8 X C_4, 15 have a class group isomorphic to C_4 X C_2 X C_2 X C_2, and the remaining 13 have a class group isomorphic to C_4 X C_4 X C_2.
%H A351670 Andy Huchala, <a href="/A351670/b351670.txt">Table of n, a(n) for n = 1..708</a>
%H A351670 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%o A351670 (Sage)
%o A351670 ls = [(QuadraticField(-n, 'a').discriminant(), QuadraticField(-n, 'a').class_number()) for n in (0..10000) if is_fundamental_discriminant(-n) and not is_square(n)];
%o A351670 [-a[0] for a in ls if a[1] == 32]
%Y A351670 Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664.
%K A351670 nonn,fini,full
%O A351670 1,1
%A A351670 _Andy Huchala_, Mar 24 2022