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

Alonso Del Arte alonso.delarte at gmail.com
Wed Oct 29 02:44:44 CET 2014

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?


P.S. I am aware of the all 1's sequence being the equivalent for UFDs.

Alonso del Arte
Author at SmashWords.com
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>

More information about the SeqFan mailing list