The Problem of the Gym Teacher

After mastering version control systems, the dedicated PE teacher at LCS developed a strong desire to preserve all his uniquely styled tables and diagrams for future use. Concerned about competitors stealing his work and distrustful of existing cryptosystems, he devised a brand-new encryption algorithm by the end of the session. However, the algorithm relies on the function $\text{AMF}(n)$ for a given natural number $n$: $\text{AMF}(n)$ is defined as the smallest natural number that is divisible by $n$ and whose digits sum up to $n$. Unfortunately, the PE teacher struggles to compute this function for n > 9, and he earnestly seeks your assistance to calculate it for values 1 \le n \le 1000.

We can't leave him to tackle this daunting challenge alone! Let's help the PE teacher!