Question 94
Let $n$ be an integer greater than $1$. Denote the first $n$ primes in increasing order by $p_1, p_2, \dots, p_n$ (i.e., $p_1 = 2, p_2 = 3, \dots$). Let $A = p_1^{p_1} p_2^{p_2} \cdots p_n^{p_n}$. Find all positive integers $x$ such that $\frac{A}{x}$ is even and has exactly $x$ distinct positive divisors.