[seqfan] Numbers expressible as a product of Fibonacci numbers

[Charles Greathouse]

A065108 lists numbers that are the product of any number of Fibonacci
numbers. How fast does this grow, asymptotically?

It's clear that it grows faster than (log n)^k for any fixed k. It
doesn't seem like this should be dense enough to grow like n^k for any
k > 0, but perhaps I could be surprised here. Surely there are
standard methods for problems like this...?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University