KöMaL 2007 B4002

Prove that if $n$>1 is an integer then there exists a sequence of integers $a_1$=$n$<$a_2$<$a_3$<..., such that $a_1 ^2$+...+$a_k ^2$ is divisible by the number $a_1$+...+$a_k$ for all values of $k$.