Question 75
For every positive integer $n$, let $\sigma(n)$ denote the number of positive divisors of $n$. Determine all positive integers $k$ such that there exist positive integers $a$ and $b$ satisfying
$$
k = \sigma(a) = \sigma(b) = \sigma(2a + 3b).
$$
$$
k = \sigma(a) = \sigma(b) = \sigma(2a + 3b).
$$