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 A096445 #12 Jul 15 2025 19:16:05 %S A096445 1,1,2,2,2,4,4,4,6,4,6,8,6,8,8,8,8,12,10,8,16,12,12,16,10,12,18,16,14, %T A096445 16,16,16,24,16,16,24,18,20,24,16,20,32,22,24,24,24,24,32,28,20,32,24, %U A096445 26,36,24,32,40,28,30,32,30,32,48,32,24 %N A096445 Number of reduced primitive positive definite binary quadratic forms of determinant n^2. %C A096445 Equivalently, of discriminant -4n^2. %H A096445 Jarrod G. Sage, <a href="/A096445/b096445.txt">Table of n, a(n) for n = 1..7000</a> %H A096445 J. H. Conway and N. J. A. Sloane, <a href="http://neilsloane.com/doc/splag.html">Sphere Packings, Lattices and Groups</a>, Springer-Verlag, 3rd edition, 1999, see Table 15.1. %H A096445 University of Cambridge, <a href="https://www.maths.cam.ac.uk/undergrad/catam/II/15pt3.pdf">Number Theory: Positive Definite Binary Quadratic Forms</a> %e A096445 There are three reduced binary quadratic forms ax^2 + bxy +cy^2, notated as (a,b,c), with a discriminant of -36 (equivalent to determinant of 9): (1,0,9); (3,0,3); and (2,1,5). (3,0,3) is not primitive, because a, b, and c are not coprime. (1,0,9) and (2,1,5) are primitive, so there are two primitive reduced binary quadratic forms with a determinant of 9. 9 is 3^2, so a(3) = 2. %Y A096445 Equals A096446(n^2). Cf. A006374. %K A096445 nonn,look %O A096445 1,3 %A A096445 _N. J. A. Sloane_, Aug 11 2004 %E A096445 a(8) onward from _Jarrod G. Sage_, Jul 11 2025