Average order of an arithmetic function: Difference between revisions

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* An average order of σ(''n''), the sum of divisors of ''n'', is ''n''π² / 6;

* An average order of φ(''n''), [[Euler's totient function]] of ''n'', is 6''n'' / π²;

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

* The average order of representations of a natural number as a sum of three squares is 4πn/3

* The average number of decompositions of a natural number into a sum of one or more consecutive prime numbers is ''nlog2''.

* An average order of ω(''n''), the number of distinct [[prime factor]]s of ''n'', is log log ''n'';

* An average order of Ω(''n''), the number of prime factors of ''n'', is log log ''n'';