I have read that some integers are not appropriate to be chosen as the modulus in an RSA cryptosystem. Some of these numbers are those that, given a modulus $n=pq$, then $p-1$ or $q-1$ do not have large factors. This is due to the fact that there are factorization algorithms that allow this type of modulus to be factored efficiently.
My question is, what other types of integers are not suitable to be used as a modulus and why?
Other kind of numbers not suitable as RSA modulus: