In [[mathematics]], especially in the field of [[number theory]], functions of [[positive integer]]s which respect products are important and are called '''completely multiplicative functions''' or '''totally multiplicative functions'''. Especially in number theory, a weaker condition is also important, respecting only products of [[coprime]] numbers, and such functions are called [[multiplicative function]]s. Outside of number theory, the term "multiplicative function" is often taken to be synonymous with "completely multiplicative function" as defined in this article.
