Editing Multiplicative function (section)

{{short description|Function equal to the product of its values on coprime factors}}
{{hatnote|Outside number theory, the term '''multiplicative function''' is usually used for [[completely multiplicative function]]s. This article discusses number theoretic multiplicative functions.}}

In [[number theory]], a '''multiplicative function''' is an [[arithmetic function]] <math>f</math> of a positive [[integer]] <math>n</math> with the property that <math>f(1)=1</math> and 
<math display="block">f(ab) = f(a)f(b)</math> whenever <math>a</math> and <math>b</math> are [[coprime]].

An arithmetic function is said to be '''[[completely multiplicative function|completely multiplicative]]''' (or '''totally multiplicative''') if <math>f(1)=1</math> and <math>f(ab) = f(a)f(b)</math> holds ''for all'' positive integers <math>a</math> and <math>b</math>, even when they are not coprime.