IN-TST 2010 Problem 5

Given an integer $k>1$ , show that there exist an integer an $n>1$ and distinct positive integers $a_1,a_2,\cdots a_n$ , all greater than $1$ , such that the sums $\sum_{j=1}^n a_j$ and $\sum_{j=1}^n \phi (a_j)$ are both $k$ -th powers of some integers. (Here $\phi (m)$ denotes the number of positive integers less than $m$ and relatively prime to $m$ .)