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A divisibility sequence related to an abelian variety isogenous to a power of an elliptic curve.
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%I #9 Oct 22 2023 16:12:20

%S 1,1,4879,38077,30072836561,107933476500157,4138965919245703746721,

%T 66133907203676573069013283,956411893315133996067203651053840799,

%U 1641203540496096533681564936955975943520959,71281475498349438098488103653467744633790545028521199

%N A divisibility sequence related to an abelian variety isogenous to a power of an elliptic curve.

%C Let E be the elliptic curve defined by y^2 = x^3 + 8*x^2 + 36*x + 288 and let P be the point (8, -40) on E. Baranczuk-Naskrecki-Verzobio proved that a(n) is the product of all primes > 5 which divide the denominator of the x-coordinate of n*P. - _Robin Visser_, Oct 22 2023

%H Stefan Baranczuk, Bartosz Naskrecki, and Matteo Verzobio, <a href="http://arxiv.org/abs/2309.09699">Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve</a>, arXiv:2309.09699 [Math.NT], Sep 18 2023.

%o (Sage)

%o def a(n):

%o E = EllipticCurve([0,8,0,36,288])

%o ans = 1

%o for pp in factor((n*E(8, -40))[0].denominator()):

%o if pp[0] > 5: ans *= pp[0]

%o return ans # _Robin Visser_, Oct 22 2023

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Oct 11 2023

%E More terms from _Robin Visser_, Oct 22 2023