The asymptotic properties of $\phi(n)$ and a problem related to visibility of Lattice points

Abstract

We look at the average sum of the Euler's phi function $\phi{(n)}$ and it's relation with the visibility of a point from the origin.We show that $\forall{\hspace{0.05in}{k} \ge{1}},k\in\mathbb{N},\exists$ a $k$$\times$$k$ grid in the 2D space such that no point inside it is visible from the origin.We define visibility of a lattice point from a set and try to find a bound for the cardinality of the smallest set S such that for a given $n$ $\in\mathbb{N}$,all points from the $n$$\times$$n$ grid are visible from S.