Average order of an arithmetic function: Difference between revisions

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

* An average order of {{math|''σ''(''n'')}}, the [[Divisor function|sum of divisors]] of {{math|''n''}}, is {{math|''n''π²{{thinsp|/}}6}};

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

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

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