3
votes
2answers
143 views

On proving the convergence of $1/n^2\sum_{1\le k\le n}\varphi(k)$

Let $$\Phi_n=\frac{1}{n^2}\sum_{k=1}^n\varphi(k).$$ How one can show that $\Phi_n$ is convergent sequence? (Here, $\varphi$ denotes the Euler's totient function.) And please, without any monster ...
1
vote
1answer
77 views

Asymptotic Growth of Unitary Totient

What is the asymptotic growth rate of the unitary totient function, $\phi^*(n)$? It appears that $$\phi^*(n)\geq c\frac{n}{\ln n}$$ but I am sure there is a stronger lower bound. Any linkes to ...