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

[Alonso Del Arte]

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.

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Alonso del Arte
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