Average order of an arithmetic function: Difference between revisions

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==Examples==<!-- &#x200A; is hair space (&hairsp; doesn't work). -->

* An average order of {{math|''d''&#x200A;(''n'')}}, the [[Divisor function|number of divisors]] of {{math|''n''}}, is {{math|log ''n''}};

* An average order of {{math|''σ''&#x200A;(''n'')}}, the [[Divisor function|sum of divisors]] of {{math|''n''}}, is {{math|''n''&#x200A;π²{{thinsp|/}}63}};

* An average order of {{math|''φ''&#x200A;(''n'')}}, [[Euler's totient function]] of {{math|''n''}}, is {{math|63&#x200A;''n''{{thinsp|/}}π²}};

* An average order of {{math|''r''&#x200A;(''n'')}}, the number of ways of expressing {{math|''n''}} as a sum of two squares, is {{math|π&#x200A;''n''}};

* The average order of representations of a natural number as a sum of three squares is {{math|4π&#x200A;''n''{{thinsp|/}}3}};