This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A046125 #44 Apr 15 2025 08:27:34
%S A046125 9,18,16,54,25,51,31,131,34,87,41,206,37,95,68,322,45,150,47,350,85,
%T A046125 139,68,511,95,190,93,457,83,255,73,708,101,219,103,668,85,237,115,
%U A046125 912,109,339,106,691,154,268,107,1365,132,345,159,770,114,427,163,1205,179,291
%N A046125 Number of negative fundamental discriminants having class number n.
%H A046125 Andy Huchala, <a href="/A046125/b046125.txt">Table of n, a(n) for n = 1..100</a> (from Watkins' paper)
%H A046125 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 A046125 K. Soundararajan, <a href="https://doi.org/10.46298/hrj.2007.157">The number of imaginary quadratic fields with a given class number</a>, Hardy-Ramanujan Journal, Vol. 30 (2007), pp. 13-18.
%H A046125 Mark Watkins, <a href="http://dx.doi.org/10.1090/S0025-5718-03-01517-5">Class numbers of imaginary quadratic fields</a>, Mathematics of Computation 73 (2004), pp. 907-938.
%H A046125 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>.
%H A046125 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>.
%F A046125 From _Amiram Eldar_, Apr 15 2025: (Start)
%F A046125 Formulas from Soundararajan (2007):
%F A046125 Sum_{k=1..n} a(k) = (3*zeta(2)/zeta(3)) * n^2 + O(n^2 * log(n)^(-1/2+eps)).
%F A046125 a(n) << n^2 * log(log(n))^4 / log(n). (End)
%e A046125 a(1) = 9 because the discriminants {-3,-4,-7,-8,-11,-19,-43,-67,-163} are the only ones with class number 1.
%t A046125 FundamentalDiscriminantQ[n_] := n != 1 && (Mod[n, 4] == 1 || ! Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via Eric E. Weisstein *);
%t A046125 k = 1; t = Table[0, {125}]; While[k < 2000001, If[ FundamentalDiscriminantQ@ -k, a = NumberFieldClassNumber@ Sqrt@ -k; If[a < 126, t[[a]]++]]; k++]; t (* _Robert G. Wilson v_ Jun 01 2011 *)
%o A046125 (PARI) lista(nn=10^7) = {my(NMAX=100, v = vector(NMAX), c); for (k=1, nn, if (isfundamental(-k), if ((c = qfbclassno(-k)) <= NMAX, v[c] ++););); v;} \\ _Michel Marcus_, Feb 17 2022
%Y A046125 Cf. A014602, A014603, A006203, A013658, A046002-A046016, A048925, A056987, A081319, A038552, A191408, A191410.
%Y A046125 Cf. A038552, A306633.
%K A046125 nonn,nice
%O A046125 1,1
%A A046125 _Eric W. Weisstein_
%E A046125 Edited by _Robert G. Wilson v_, May 13 2003
%E A046125 Corrected and extended by _Dean Hickerson_, May 20 2003. The values were obtained by transcribing and combining data from Tables 1-3 of Buell's paper, which has information for all values of n up to 125.