%I #29 Jun 02 2023 01:56:49
%S 5,7,1,5,1,1,3,9,5,5,3,1,1,5,1,5,1,7,1,1,3,3,3,1,5,3,1,5,1,1,1,9,5,3,
%T 3,5,5,3,1,5,1,1,1,3,1,3,1,1,5,7,1,1,1,1,1,7,7,1,1,1,1,1,3,5,17,1,1,1,
%U 1,5,3,9,1,3,1,1,1,9,1,1,5,1,1,5,1,3,1,5,1,5,5,3,1,1,3,1,1
%N Number of integral solutions to Mordell's equation y^2 = x^3 + n^3.
%H Max Alekseyev, <a href="/A356706/b356706.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = A081119(n^3).
%e a(8) = 9 since the equation y^2 = x^3 + 8^3 has 9 integral solutions (-8,0), (-7,+-13), (4,+-24), (8,+-32), and (184,+-2496).
%o (SageMath) [len(EllipticCurve(QQ, [0, n^3]).integral_points(both_signs=True)) for n in range(1, 61)] # _Lucas A. Brown_, Sep 03 2022
%Y Cf. A081119, A356707, A356708.
%Y Indices of 1, 3, 5, and 7: A356709, A356710, A356711, A356712.
%K nonn,hard
%O 1,1
%A _Jianing Song_, Aug 23 2022
%E a(21) corrected and a(22)-a(60) from _Lucas A. Brown_, Sep 03 2022
%E Terms a(61) onward from _Max Alekseyev_, Jun 01 2023