Isn't it weird that nobody's mentioned so far K. Chandrasekharan's treatise on Arithmetic Functions? OK, they've already mentioned his book on the principles of Analytic Number Theory, yet the book I'm now referring to is
K. Chandrasekharan. Arithmetical Functions. Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen, Band 167, Springer-Verlag.
You should definitely take a look at it, esteemed rpg16! I consider that none of the texts listed above is more to the point than this one.