[seqfan] Enumerating tuples of pariwise coprime numbers ?

[Rémy Etc]

Dear Sequence Fans,

I recently submitted a sequence briefly describing a method to uniquely
enumerate, for some given t > 0, every tuple of t pariwise coprime numbers
:A289815.

For the case t=2, there are several well known methods to enumerate pairs
of coprime numbers, for example, A002487, Stern's diatomic series.

Do you know other methods for cases t > 2 ?

Best regards,

Rémy Sigrist