CONO-SUR 2015 Problem 5

Determine if there exists an infinite sequence of not necessarily distinct positive integers $a_1, a_2, a_3,\ldots$ such that for any positive integers $m$ and $n$ where $1 \leq m < n$ , the number $a_{m+1} + a_{m+2} + \ldots + a_{n}$ is not divisible by $a_1 + a_2 + \ldots + a_m$ .