Nested Candy Boxes

Andy got a box of candies for Christmas. In fact, he discovered that the box contained several identical smaller boxes, and they could contain even smaller boxes, and so on. Formally, we say that candies are boxes of level 0, and for $1 \leq i \leq n$, a level $i$ box contains $a_i$ boxes of level $i-1$. The largest box has level $n$. Andy realized that it can take quite a long time to open all th