  We study the notion of Beurling-Malliavin density from the point of view of
Number Theory. We prove a general relation between the Beurling-Malliavin
density and the upper asymptotic density; we identify a class of sequences for
which the two densities coincide; this class contains the arithmetic
progressions. Last, by means of an alternative definition of Beurling-Malliavin
density, we study the connection with the asymptotic density for another kind
of sequences that again generalizes the arithmentic progressions.
