The arithmetic functions which are used in number theory and specifically by number theorist are of special significance. I've seen many important research articles and famous proofs posed by mathematical giants , all were cruising smooth with arithmetic functions.
Please suggest me some good reference books / materials from which I can learn how to use those arithmetic functions , I've read about them on Wikipedia but find it really hard to manipulate because each has its own special properties, now where and how to use it to arrive at some specific result is what I find difficult, so if possible please put some beautiful examples of different approaches to arrive at some results using arithmetic functions.
Thanks in advance Regards!
The book Introduction to Arithmetical Functions by Paul J. McCarthy contains a lot of different arithmetical functions providing a nice introduction to the subject.