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 A356706 Number of integral solutions to Mordell's equation y^2 = x^3 + n^3. 8
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Max Alekseyev, Table of n, a(n) for n = 1..100 FORMULA a(n) = A081119(n^3). EXAMPLE 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). PROG (SageMath) [len(EllipticCurve(QQ, [0, n^3]).integral_points(both_signs=True)) for n in range(1, 61)] # Lucas A. Brown, Sep 03 2022 CROSSREFS Cf. A081119, A356707, A356708. Indices of 1, 3, 5, and 7: A356709, A356710, A356711, A356712. Sequence in context: A323386 A021179 A153613 * A318375 A023571 A160631 Adjacent sequences: A356703 A356704 A356705 * A356707 A356708 A356709 KEYWORD nonn,hard AUTHOR Jianing Song, Aug 23 2022 EXTENSIONS a(21) corrected and a(22)-a(60) from Lucas A. Brown, Sep 03 2022 Terms a(61) onward from Max Alekseyev, Jun 01 2023 STATUS approved

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Last modified August 3 23:57 EDT 2024. Contains 374905 sequences. (Running on oeis4.)