## Is an=1n∑nk=1φ(k)ka_n=\frac{1}{n}\sum_{k=1}^n\frac{\varphi(k)}{k} convergent?

Let (an)n∈N be defined as an=1n∑nk=1φ(k)k where φ is the euler totient function. Is (an) convergent. If so, what is its limit? I have checked it numerically; it seems to converge to the value a≈0.6079384135652464404586775568799731914204890312331725 However, I cannot think of a way to prove it. Answer Here you can find that the value you’re looking … Read more