# [seqfan] Re: A344826

David Corneth davidacorneth at gmail.com
Tue Jun 15 12:47:57 CEST 2021

```One interesting property could be that prime powers used are fairly small.
If fairly small could be defined that's interesting. Known data have the
largest prime power factor 3^7 = 2187 and the largest prime factor 71.
Computationally there might be some tricks at hand. Like if a(n) is
divisible by 11 then it must be divisible by at least one of 9, 42, 245,
... indices of powers of 11 in A000961 larger than 1
If it's divisible by 245 then it's divisible by lcm(245,11) = 2695 and also
by one of 5, 15, 43, 137, ... (indices of powers of powers of 5 in A000961
larger than 1).
If it's divisible by 137 then a(n) is also divisible by lcm(2695, 137)
= 369215.
Maybe with some refining this method could speed the search up a little to
at least get upperbounds of other terms or maybe even actual proven new
terms.

On Mon, Jun 14, 2021 at 6:13 PM Tom Duff <eigenvectors at gmail.com> wrote:

> I think my question wasn't clear enough.
> Why is this a mathematically interesting sequence?
> Is the sequence related to some mathematically interesting problem?
> Does it shed light on some important question?
> The number of terms in the b file doesn't address those questions.
>
> I'm unlikely to be interested in undertaking a long computation if it
> doesn't provide some mathematical insight.
>
> On Sat, Jun 12, 2021 at 1:44 PM <michel.marcus at free.fr> wrote:
> >
> > Well, I see several reasons:
> > 90 terms for A344826 and A343886 is not much; 2*10^8 is not that big too.
> > they are similar to A127724 and so somehow to A127724 (but of course,
> with a different function).
> > my pari script is limited to the allocatemem I can do, maybe someone has
> better.
> > I tried to save the underlying data in files to counteract my memory
> limitation but when n increase, it kept switching files, so it did not work.
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```