linguistic:translation
Examples

Some multiplicative functions are defined to make formulas easier to write:

Other examples of multiplicative functions include many functions of importance in number theory, such as:

An example of a non-multiplicative function is the arithmetic function r (n) - the number of representations of n as a sum of squares of two integers, positive, negative, or zero, where in counting the number of ways, reversal of order is allowed. For example:

and therefore r (1) = 4 ≠ 1. This shows that the function is not multiplicative. However, r (n)/4 is multiplicative.

In the On-Line Encyclopedia of Integer Sequences, sequences of values of a multiplicative function have the keyword "mult".

See arithmetic function for some other examples of non-multiplicative functions.