A309142 Rank of elliptic curve y^2 = x^3 + (n^2 - 6*n -3)*x^2 + 16*n*x.

0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1

Offset: 10

Author

Seiichi Manyama, Jul 14 2019

Keywords

• nonn

Comments

a(n) is undefined for n = 0, 1 or 9.

Links

• Jinyuan Wang, Table of n, a(n) for n = 10..5000
• Andrew Bremner, Richard K. Guy, Richard J. Nowakowski, Which integers are representable as the product of the sum of three integers with the sum of their reciprocals?, Math. Comp. 61 (1993), 117-130.
• Allan J. MacLeod, Knight's Problem

Crossrefs

Cf. A085514, A086446, A309143, A309144, A309146.

Programs

PARI

{a(n) = ellanalyticrank(ellinit([0, n^2-6*n-3, 0, 16*n, 0]))[1]}