Let $D(n)$ denote the number of ways of writing the positive integer $n$ as a product

$n=f_1\cdot f_2\cdots f_k$,

where $k\ge 1$, the $f_i$ are integers strictly greater than $1$, and the order in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct). What is $D(256)$?