# [seqfan] Re: Sequences counting distinct factorizations in a non-UFD

Alonso Del Arte alonso.delarte at gmail.com
Wed Oct 29 02:46:27 CET 2014

```Should've written "2 * 3 * (4 - sqrt(10))(4 + sqrt(10)) count as a distinct
factorization apart from 2^2 * 3^2 and (4 - sqrt(10))^2 (4 + sqrt(10))^2"
in  that previous message. Sorry.

On Tue, Oct 28, 2014 at 9:44 PM, Alonso Del Arte <alonso.delarte at gmail.com>
wrote:

> I suspect some sequences like this one, if not exactly this one, are
> already in the OEIS, but I haven't had the time to sit down to work out the
> theory and verify the identifications:
>
> a(n) counts how many distinct factorizations n has in Z[sqrt(10)].
>
> It is a very well-known fact that a(6) = 2.
>
> But I haven't seen discussion anywhere of what a(36) is. Does 6 * (4 -
> sqrt(10))(4 + sqrt(10)) count as a distinct factorization apart from 6^2
> and (4 - sqrt(10))^2 (4 + sqrt(10))^2? Should it count?
>
> Al
>
> P.S. I am aware of the all 1's sequence being the equivalent for UFDs.
>
> --
> Alonso del Arte
> Author at SmashWords.com
> <https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>

--
Alonso del Arte
Author at SmashWords.com
<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>

```