Good books on arithmetic functions?
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.
A MathSciNet search set to Books and with "arithmetic functions" entered into the "Anywhere" field yields 148 matches. Some of the more promising ones:
The theory of arithmetic functions. Proceedings of the Conference at Western Michigan University, Kalamazoo, Mich., April 29--May 1, 1971. Edited by Anthony A. Gioia and Donald L. Goldsmith. Lecture Notes in Mathematics, Vol. 251. Springer-Verlag, Berlin-New York, 1972. v+287 pp.
$ $
Narkiewicz, Wƚadysƚaw Elementary and analytic theory of algebraic numbers. Monografie Matematyczne, Tom 57. PWN---Polish Scientific Publishers, Warsaw, 1974. 630 pp. (errata insert).
$ $
Babu, Gutti Jogesh Probabilistic methods in the theory of arithmetic functions. Macmillan Lectures in Mathematics, 2. Macmillan Co. of India, Ltd., New Delhi, 1978.
$ $
Elliott, P. D. T. A. Arithmetic functions and integer products. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 272. Springer-Verlag, New York, 1985.
$ $
Sivaramakrishnan, R. Classical theory of arithmetic functions. Monographs and Textbooks in Pure and Applied Mathematics, 126. Marcel Dekker, Inc., New York, 1989.
$ $
Schwarz, Wolfgang; Spilker, Jürgen Arithmetical functions. An introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties. London Mathematical Society Lecture Note Series, 184. Cambridge University Press, Cambridge, 1994.
$ $
Tenenbaum, Gérald Introduction to analytic and probabilistic number theory. Translated from the second French edition (1995) by C. B. Thomas. Cambridge Studies in Advanced Mathematics, 46. Cambridge University Press, Cambridge, 1995.
There's also this one: McCarthy, Paul J. Introduction to arithmetical functions. Springer, 1986.