ISL 2020 N6

For a positive integer $n$, let $d(n)$ be the number of positive divisors of $n$, and let $\varphi(n)$ be the number of positive integers not exceeding $n$ which are coprime to $n$. Does there exist a constant $C$ such that $$\frac{\varphi(d(n))}{d(\varphi(n))} \leqslant C$$ for all $n \geqslant 1$ ? (Cyprus)