Question 87
Find all positive integers $n$ with the following property: there is a permutation $(d_1, d_2, \dots, d_k)$ of all the positive divisors of $n$ (there are $k$ of them) such that for every $i = 1, 2, \dots, k$, the integer $\sum_{j=1}^{i} d_j = d_1 + \dots + d_i$ is a perfect square.