MathNet 2012 Question 11

A sequence $a_1, a_2, \dots$ is defined in the following way: $a_1 = 1$, $a_2 = 143$, and $a_{n+1} = 5 \cdot \frac{a_1 + a_2 + \dots + a_n}{n}$ for $n \ge 2$. Prove that $a_n$ is an integer for every $n \ge 1$.