[seqfan] Numbers that are divisible by the product of their digits

[Charles Greathouse]

A007602 is the sequence of numbers that are divisible by the product of
their digits. Does anyone know how this sequence grows?

The sequence is infinite, as it contains the repunits. You can get a very
weak bound by taking numbers with two 3s and 9k+3 1s: this shows there are
at least n^3/54 +O(n^2) terms with up to n digits, so log a(n) << n^(1/3).
But surely more is true?

My interest comes from a recent submission I just approved, A288069, which
are the quotients in this sequence. The quotients go to infinity, but I
can't give a rate of growth on the quotients without knowing the rate of
growth of the underlying sequence.

Charles Greathouse
Case Western Reserve University