Question 55
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 every $n\geq1$?
$$
\frac{\varphi(d(n))}{d(\varphi(n))}\leq C
$$
for every $n\geq1$?