Before revision:  Motivated by the study of the mixing set problem and a recent result in the field of real-time systems we investigate the case of harmonic divisors, i.e. a_{i+1}/a_i is an integer for all i<n  .
After revision:  Motivated by the study of the mixing set problem and a recent result in the field of real-time systems we investigate the case of harmonic divisors, i.e. a_{i+1}/a_i is an integer for all i<n , which was heavily studied for the mixing set problem as well, we also answer a recent algorithmic question from the field of real-time systems .