Question 2
Let $ n \geqslant 2 $ be a positive integer, with divisors $ 1 = d_1 \lt d_2 \lt \ldots \lt d_k = n $. Prove that $ d_1d_2 + d_2d_3 + \ldots + d_{k-1}d_k $ is always less than $ n^2 $, and determine when it is a divisor of $ n^2 $.