[seqfan] Re: A337036

David Corneth davidacorneth at gmail.com
Mon Nov 16 19:57:40 CET 2020

```Maybe make a list of such tuples (x, y, z, w) whose lcm is <= some chosen
U. Note that you can use that x^3 + y^3 + z^3 = w^3 gives x^3 + y^3 = w^3 -
z^3 = (w-z)(w^2 + z*w + z^2) which may ease the search for such tuples. You
can then check each divisor of some candidate c if it's part of some known
tuple. Like there is the tuple (1, 6, 8, 9) which has an lcm of 72 so any
number having that in its divisors must be divisible by 72. That way you
can pick tuples to check for a certain candidate.
The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. We can
check 1 is part of a tuple via (1, 6, 8, 9), 2 isn't via 2*(1, 6, 8, 9) =
(2, 12, 16, 18) as 72 isn't divisible by 16 and also via no other tuple. As
6 is part of a tuple and is bigger than 2, 72 isn't in the sequence. Maybe
play around and see what you get if you like.

Any terms that aren't 5-smooth?

Best,
David

On Sun, Nov 15, 2020 at 6:51 PM <michel.marcus at free.fr> wrote:

>
> It appears that all terms in A337036 are mutiple of 6 (property used by
> the Maple program).
> I added a b-file today but with just one more term than listed in the pdf
> a-file (I did not use the above property).
> Can we rely on this property to speed up the search ? Or a higher value as
> suggested by the conjecture 1 in the comments ?
>
>
> Thanks
> MM
>
>
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```