Average order of an arithmetic function: Difference between revisions

Revision as of 23:49, 5 May 2012

Revision as of 21:08, 12 June 2012

Line 16:

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

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

* The [[prime number theorem]] is equivalent to the statement that the [[von Mangoldt function]] Λ(''n'') has average order 1.;

* The average order of μ(''n''), the [[Möbius function]], is zero; this is again equivalent to the [[prime number theorem]].

==See also==