RS-SMO 2024 Problem 1

Find all positive integers $n$ , such that if their divisors are $1=d_1<d_2<\ldots<d_k=n$ for $k \geq 4$ , then the numbers $d_2-d_1, d_3-d_2, \ldots, d_k-d_{k-1}$ form a geometric progression in some order.