 Note that since formula_2 as formula_3 (see Prime zeta function), this is also equal to

This expression is usually the order of the "pole" of

at "s" = 1, (though in general it is not really a pole as it has non-integral order), at least if this function is a holomorphic function times a (real) power of "s"−1 near "s" = 1.For example, if "A" is the set of all primes, it is the Riemann zeta function which has a pole of order 1 at "s" = 1, so the set of all primes has Dirichlet density 1.More generally, one can define the Dirichlet density of a sequence of primes (or prime powers), possibly with repetitions, in the same way.