KöMaL 2024 B5366

Is it possible to find a composite number $n>1$ with the following property: if $1=d_1<d_2<\ldots<d_k=n$ denote the positive divisors of $n$, then $d_i$ is divisible by $(d_{i-1} + d_{i-2})$ for all $3 \leq i \leq k$?