Multiplicative function: Difference between revisions

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{{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 multiplicativetetiplicative function]]s. This article discusses number theoretic multiplicative functions.}}

In [[number theory]], a '''multiplicative function'''mu 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]].