Totient summatory function: Difference between revisions
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Let <math>x</math> be a positive real number. The '''totient summatory function''' of <math>x</math> is defined as: | Let <math>x</math> be a positive real number. The '''totient summatory function''' of <math>x</math> is defined as: | ||
<math>\Phi(x) = \sum_{n \le x | <math>\Phi(x) = \sum_{n \le x} \varphi(n)</math> | ||
where <math>\varphi</math> is the [[defining ingredient::Euler phi-function]]. | where <math>\varphi</math> is the [[defining ingredient::Euler phi-function]]. | ||
Latest revision as of 04:08, 29 April 2009
This article is about a function defined on positive reals (and in particular, natural numbers) obtained as the summatory function of an arithmetic function, namely Euler phi-function.
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Definition
Let be a positive real number. The totient summatory function of is defined as:
where is the Euler phi-function.
