login
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
OFFSET
1,1
LINKS
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
Indices of 1, 3, 5, and 7: A356709, A356710, A356711, A356712.
Sequence in context: A323386 A021179 A153613 * A318375 A023571 A160631
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