Question 98
Find all positive integers $n$ such that $\frac{\phi(n)^{d(n)} + 1}{n}$ is an integer and $\frac{n^{\phi(n)} - 1}{d(n)^5}$ is not. Here, $\phi(n)$ denotes the number of integers in $\{1, \dots, n\}$ coprime to $n$, and $d(n)$ denotes the number of positive divisors of $n$.