MathNet 2023-part-01 — 191 problems (EN–VI) Question 4

A sequence of integers is defined as follows: $a_1 = 1$, $a_2 = 2$, and for each $n \ge 2$, $a_{n+1}$ is equal to the greatest prime divisor of $a_1 + a_2 + \dots + a_n$. Compute $a_{100}$.