Question 31
Determine all composite positive integers $n$ with the following property: If $1 = d_1 \lt d_2 \lt \dots \lt d_k = n$ are all the positive divisors of $n$, then
$$
(d_2 - d_1) : (d_3 - d_2) : \dots : (d_k - d_{k-1}) = 1 : 2 : \dots : (k-1).
$$
$$
(d_2 - d_1) : (d_3 - d_2) : \dots : (d_k - d_{k-1}) = 1 : 2 : \dots : (k-1).
$$