Problem 3. We will call a composite natural number $n$ "interesting" if all its natural divisors can be written in ascending order, and each subsequent divisor is divisible by the previous one. Find all "interesting" natural numbers from 20 to 90 (inclusive).
Answer: $25,27,32,49,64,81$.

Solution. "Interesting" can only be numbers of the form $n=p^{k}, k=2,3,4, \ldots$, where $p-$ is a prime number.

Indeed, if we consider the number $n=a \cdot p^{k}$, GCD $(a, p)=1$, then in the sequence of divisors $1, p, \ldots, p^{k}$, the divisor $a$ cannot stand. The situation $\ldots p^{k}<a<a p \ldots$ is also impossible, since $p^{k}$ does not divide $a$. Therefore, to get the answer, we need to list all powers of prime numbers in the range from 20 to 90.