Average order of an arithmetic function: Difference between revisions

Revision as of 04:14, 17 May 2009

Revision as of 20:48, 29 July 2009

Line 11:

==Examples==

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

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

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

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

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