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Whoops, messed up the slope for sigma. Should be pi^2/12 |
The average order of r(n) is pi, while its cumulative sum grows as pi*n + O(sqrt(n)). |
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* An average order of {{math|''σ'' (''n'')}}, the [[Divisor function|sum of divisors]] of {{math|''n''}}, is {{math|''n'' π<sup>2</sup>{{thinsp|/}}12}};
* An average order of {{math|''φ'' (''n'')}}, [[Euler's totient function]] of {{math|''n''}}, is {{math|3 ''n''{{thinsp|/}}π<sup>2</sup>}};
* 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}};
* The average number of decompositions of a natural number into a sum of one or more consecutive prime numbers is {{math|''n'' log 2}};
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