<p>We solve Boshernitzan’s problem of characterization (in terms of so called Furstenberg systems) of bounded sequences that are orthogonal to all uniquely ergodic systems. As a step toward this solution, we provide a characterization of automorphisms which are disjoint from all ergodic ones as those whose a.a. ergodic components form a family of pairwise disjoint automorphisms. Some variations of Boshernitzan’s problem involving characteristic classes are considered. As an application, we characterize sequences orthogonal to all uniquely ergodic systems whose (unique) invariant measure yields a discrete spectrum automorphism as those satisfying an averaged Chowla property.</p>