Question 32
For a positive integer $n$, we define $\alpha(n)$ as the average of all positive divisors of $n$, and $\beta(n)$ as the average of all positive integers $k \le n$ such that $\gcd(k, n) = 1$.
Find all positive integers $n$ for which $\alpha(n) = \beta(n)$.
Find all positive integers $n$ for which $\alpha(n) = \beta(n)$.