Totient summatory function

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.
View other such summations

Definition

Let $x$ be a positive real number. The totient summatory function of $x$ is defined as:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi(x) = \sum_{n \le x) \varphi(n)}

where $\varphi$ is the Euler phi-function.