Let S denote a set of positive integers and τ : S → be defined so that τ(s) is a proper divisor of s (that is, τ(s) divides s and τ (s) < s). The ensemble (S, τ ) is said to have the ‘distinct divisor property’ if τ is injective, that is, if the τ (s) are different for different values of s. We will also say that S has the distinct divisor property if there exists a τ , as above, such that (S, ...
