Numerical semigroups are the cofinite subsemigroups of the natural numbers containing 0. We discuss the concept of counting numerical semigroups and introduce the notion of counting by the maximum primitive (generator) of the semigroup. For any positive integer $n$, let $A_n$ denote the set of numerical semigroups whose maximum primitive is $n$, and let $N_f$ denote the set of numerical semigroups whose Frobenius number is $f$. We show that the sequence $(|A_n|)$ is the Möbius transform of the sequence $(|N_f|)$. We discuss some further properties of the set $A_n$, and show that as n tends to infinity almost all semigroups in $A_n$ satisfy Wilf's conjecture.