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{{r|Arithmetic function}}

...athematics]], in the field of [[number theory]], the '''normal order of an arithmetic function''' is some simpler or better-understood function which "usually" takes the * [[Average order of an arithmetic function]]

{{r|Arithmetic function}}

...thematics]], in the field of [[number theory]], the '''average order of an arithmetic function''' is some simpler or better-understood function which takes the same value

* The [[Average order of an arithmetic function|average order]] of &phi;(''n'') is <math>\frac{6}{\pi^2} n</math>.

* The [[Average order of an arithmetic function|average order]] of ''J''_''k''(''n'') is ''c''&nbsp;''n''<sup>''k

The [[Average order of an arithmetic function|average order]] of σ(''n'') is <math> \frac{\pi^2}{6} n</math>.

{{r|Arithmetic function}}

{{r|Arithmetic function}}

{{r|Arithmetic function}}

{{r|Arithmetic function}}

...ties of the associated [[Dirichlet series]]. It is used in the study of [[arithmetic function]]s and yields a proof of the [[Prime number theorem]]. It is an example of

{{r|Arithmetic function}}

{{r|Arithmetic function}}

* The [[Hardy–Ramanujan theorem]] that the [[normal order of an arithmetic function|normal order]] of &omega;(''n''), the number of distinct [[prime factor]]s