Question 28
For any positive integer $n$, let $a_1, a_2, \dots, a_m$ be all the positive divisors of $n$, where $m \ge 1$. If there exist $m$ integers $b_1, b_2, \dots, b_m$ such that $n = \sum_{i=1}^{m} (-1)^{b_i} a_i$, then we say that $n$ is a *good number*. Prove that there exists a good number with exactly 2013 distinct prime factors.