Full Idea
We can view "the number of x's such that ...x..." as a functional expression that is completed by a first-level predicate and yields a name (which is of the right kind to denote an object).
Gist of Idea
"Number of x's such that ..x.." is a functional expression, yielding a name when completed
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.27
A Reaction
This is how Frege gets, in his account, from numbers being predicates to numbers being objects. He was a clever lad.