Question 44
For positive integers $n$, let $f(n)$ be the product of the digits of $n$. Find the largest positive integer $m$ such that
$$
\sum_{n=1}^{\infty} \frac{f(n)}{m^{\left\lfloor\log_{10} n\right\rfloor}}
$$
is an integer.
$$
\sum_{n=1}^{\infty} \frac{f(n)}{m^{\left\lfloor\log_{10} n\right\rfloor}}
$$
is an integer.