UA-UMO 2023 Problem 117

For a positive integer $n$ consider all its divisors $1 = d_1 < d_2 < \ldots < d_k = n$ . For $2 \le i \le k-1$ , let's call divisor $d_i$ good, if $d_{i-1}d_{i+1}$ isn't divisible by $d_i$ . Find all $n$ , such that the number of their good divisors is smaller than the number of their prime distinct divisors.

Proposed by Mykhailo Shtandenko