6 Arithmetic Functions
“Mathematics is the queen of sciences and number theory is the queen of mathematics.”
– Carl Friedrich Gauss
6.1 Introduction
There are few functions of special importance in connection with the study of the divisors of an integer. Any function whose domain of definition is the set of integers is known as the arithmetic function.
Present chapter treats multiplicative functions defined on integers, having the property that there is value at the product of two relatively prime integers equal to the product of the value of the function at these integers. In this chapter several results about multiplicative functions are done that will be used later on. We also define the sum of divisors and the number of divisors functions. ...
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