Question 172
A sequence $\{a_n\}_{n \geq 1}$ of positive integers satisfies the recurrence relation $a_{n+1} = n \left\lfloor \frac{a_n}{n} \right\rfloor + 1$ for all integers $n \geq 1$. If $a_4 = 34$, find the sum of all the possible values of $a_1$.