Surjectivity conjecture for the group enumeration function

Let $f(n)$ denote the number of isomorphism classes of finite groups of order $n$. Surjectivity conjecture. For every positive integer $m$, there exists an integer $n$ such that

$$f(n)=m.$$

This conjecture asks whether every positive integer occurs as the number of groups of some order. The surrounding discussion concerns known formulas and bounds for $f(n)$, but gives no resolution of this surjectivity question.