2020 IMO Shortlist 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 $$\frac{\varphi(d(n))}{d(\varphi(n))} \leq C$$ for all $n \geq 1$ ? (Cyprus)

对于正整数 $n$，设 $d(n)$ 为 $n$ 的正因数数，设 $\varphi(n)$ 为不超过 $n$ 且与 $n$ 互质的正整数数。是否存在一个常数 $C$ 使得 $$\frac{\varphi(d(n))}{d(\varphi(n))} \leq C$$ 对于所有 $n \geq 1$ ？ (塞浦路斯)