Question 124
For a positive integer $n$, let $d(n)$ be the number of positive divisors of $n$. Determine the positive integers $k$ for which there exist positive integers $a$ and $b$ satisfying
$$
k = d(a) = d(b) = d(2a + 3b).
$$
$$
k = d(a) = d(b) = d(2a + 3b).
$$