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 A356707 #25 Jun 06 2023 15:36:10 %S A356707 2,3,0,2,0,0,1,4,2,2,1,0,0,2,0,2,0,3,0,0,1,1,1,0,2,1,0,2,0,0,0,4,2,1, %T A356707 1,2,2,1,0,2,0,0,0,1,0,1,0,0,2,3,0,0,0,0,0,3,3,0,0,0,0,0,1,2,8,0,0,0, %U A356707 0,2,1,4,0,1,0,0,0,4,0,0,2,0,0,2,0,1,0,2,0,2,2,1,0,0,1,0,0,3,1,2 %N A356707 Number of integral solutions to Mordell's equation y^2 = x^3 + n^3 with y positive. %C A356707 Equivalently, number of different values of x in the integral solutions to the Mordell's equation y^2 = x^3 + n^3 apart from the trivial solution (-n,0). %F A356707 a(n) = (A081119(n^3)-1)/2 = (A356706(n)-1)/2 = A356706(n) - A356708(n). %e A356707 a(2) = 3 because the solutions to y^2 = x^3 + 2^3 with y > 0 are (1,3), (2,4), and (46,312). %o A356707 (SageMath) [(len(EllipticCurve(QQ, [0, n^3]).integral_points(both_signs=True))-1)/2 for n in range(1, 61)] # _Lucas A. Brown_, Sep 03 2022 %Y A356707 Cf. A081119, A356706, A356708. %Y A356707 Indices of 0, 1, 2, and 3: A356709, A356710, A356711, A356712. %K A356707 nonn,hard %O A356707 1,1 %A A356707 _Jianing Song_, Aug 23 2022 %E A356707 Offset and a(21) corrected and a(22)-a(60) by _Lucas A. Brown_, Sep 03 2022 %E A356707 a(61)-a(100) from _Max Alekseyev_, Jun 01 2023