KöMaL 2026 B5522

Does there exist a sequence of positive integers $a_1$, $a_2$, $\ldots$ and positive integer $N$ such that for every $n\geq N$, $a_n<a_{n+1}<{a_1+a_2+\ldots+a_n}$ and $a_{n+1}\mid a_1+a_2+\ldots+a_n$?