MathNet 1989 — Part 01 Question 43

A positive integer $n$ has exactly $12$ positive divisors $1 = d_1 \lt d_2 \lt d_3 \lt \ldots \lt d_{12} = n$. Let $m = d_4 - 1$. We have $d_m = (d_1 + d_2 + d_4) d_8$. Find $n$.