Question 50
Let $\varphi(n)$ denote the number of positive integers less than or equal to $n$ which are relatively prime to $n$. Let $S$ be the set of positive integers $n$ such that $\frac{2 n}{\varphi(n)}$ is an integer. Compute the sum
$$
\sum_{n \in S} \frac{1}{n}
$$
$$
\sum_{n \in S} \frac{1}{n}
$$