2023 IMO Shortlist N1

Determine all positive, composite integers $n$ that satisfy the following property: if the positive divisors of $n$ are $1=d_{1}<d_{2}<\cdots<d_{k}=n$, then $d_{i}$ divides $d_{i+1}+d_{i+2}$ for every $1 \leq i \leq k-2$. (Colombia)

确定满足以下属性的所有正复合整数 $n$：如果 $n$ 的正因数为 $1=d_{1}<d_{2}<\cdots<d_{k}=n$，则 $d_{i}$ 可以除以 $d_{i+1}+d_{i+2}$，每 $1 \leq i \leq k-2$。 (哥伦比亚)