A356706 - OEIS

A356706

Number of integral solutions to Mordell's equation y^2 = x^3 + n^3.

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