

A283564


Positive integers k such that k = a/(b+c) + b/(a+c) + c/(a+b) for some positive integers a, b and c where the corresponding elliptic curve has rank=1.


1



4, 6, 10, 12, 14, 16, 18, 24, 28, 32, 38, 42, 46, 48, 58, 60, 66, 76, 82, 92, 102, 112, 116, 126, 130, 132, 136, 146, 156, 158, 162, 178, 182, 184, 186, 196, 198, 200
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OFFSET

1,1


COMMENTS

There are no odd numbers in this sequence.
The values for a, b and c are very large. The smallest known solutions contain 81 digits (for k=4).


LINKS

Table of n, a(n) for n=1..38.
Alon Amit, How do you find the positive integer solutions to ...?, Quora, Aug 07, 2017 [Broken link]
Andrew Bremner and Allan Macleod, An Unusual Cubic Representation Problem, Annales Mathematicae et Informaticae, volume 43 (2014), pages 2941, see Table 2 page 38.
Mathoverflow, Estimating the size of solutions of a diophantine equation
Physics Forums, Find positive integer solutions to a/(b+c)+b/(a+c)+c/(a+b)=4, Aug 06 2017
Jinyuan Wang, PARI program and details of k = 4, 6, 10, 12, 14


CROSSREFS

Sequence in context: A163164 A120351 A137230 * A181794 A199536 A284883
Adjacent sequences: A283561 A283562 A283563 * A283565 A283566 A283567


KEYWORD

nonn,more


AUTHOR

Dmitry Kamenetsky, Mar 11 2017


EXTENSIONS

Definition clarified by Jimmy Gustafsson, May 08 2019


STATUS

approved



