  The squarefree flow is a natural dynamical system whose topological and
ergodic properties are closely linked to the behavior of squarefree numbers. We
prove that the squarefree flow carries a unique measure of maximal entropy and
express this measure explicitly in terms of a skew-product of a Kronecker and a
Bernoulli system. Using this characterization and a number-theoretic argument,
we then show that the unique maximum entropy measure fails to possess the Gibbs
property.
