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nonn,hard,more,changed

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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, 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, 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

a(61)-a(100) from Max Alekseyev, Jun 01 2023

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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, 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

01,1

a(2) = 3 because the solutions to y^2 = x^3 + 2^3 with y > 0 are (1,3), (2,4), and (46,312).

(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

Offset and a(21) corrected and a(22)-a(60) by Lucas A. Brown, Sep 03 2022

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Lucas A. Brown: Sage cannot currently compute a(61).

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