A351670 - OEIS

%I #9 Mar 27 2022 22:55:00

%S 791,1119,1239,1463,1551,1767,1784,1943,2084,2180,2276,2343,2840,2847,

%T 2996,3080,3156,3199,3207,3236,3247,3295,3428,3476,3679,3812,3895,

%U 4088,4296,4340,4495,4584,4647,4767,4868,4884,4964,4980,4996,5012,5064,5192,5215

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

%C Sequence contains 708 terms; largest is 164803.

%C 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 Andy Huchala, <a href="/A351670/b351670.txt">Table of n, a(n) for n = 1..708</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number</a>

%o (Sage)

%o 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 [-a[0] for a in ls if a[1] == 32]

%Y Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664.

%K nonn,fini,full

%O 1,1

%A _Andy Huchala_, Mar 24 2022