Average order of the Euler Totient Function
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\sum_{n\leq x}\varphi(n)=\frac{3}{\pi^2}x^2+\mathcal{O}(x\log x)
As is often the case with several functions in number theory, the values of φ(n) fluctuate considerably as n increases.
For this reason, it is more fruitful to study the arithmetic mean. Averages smooth out fluctuations, so it is reasonable to expect more regularity. This is certainly true for the Euler Totient Function.
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