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.

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Narkiewicz, Wƚadysƚaw Elementary and analytic theory of algebraic numbers. Monografie Matematyczne, Tom 57. PWN---Polish Scientific Publishers, Warsaw, 1974. 630 pp. (errata insert).

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Babu, Gutti Jogesh
Probabilistic methods in the theory of arithmetic functions.
Macmillan Lectures in Mathematics, 2. Macmillan Co. of India, Ltd., New Delhi, 1978.

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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.

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Sivaramakrishnan, R. Classical theory of arithmetic functions. Monographs and Textbooks in Pure and Applied Mathematics, 126. Marcel Dekker, Inc., New York, 1989.

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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.

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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.