  For a fixed $b\in\mathbb{N}=\{1,2,3,\ldots\}$ we say that a point $(r,s)$ in
the integer lattice $\mathbb{Z} \times \mathbb{Z}$ is $b$-visible from the
origin if it lies on the graph of a power function $f(x)=ax^b$ with
$a\in\mathbb{Q}$ and no other integer lattice point lies on this curve (i.e.,
line of sight) between $(0,0)$ and $(r,s)$. We prove that the proportion of
$b$-visible integer lattice points is given by $1/\zeta(b+1)$, where $\zeta(s)$
denotes the Riemann zeta function. We also show that even though the proportion
of $b$-visible lattice points approaches $1$ as $b$ approaches infinity, there
exist arbitrarily large rectangular arrays of $b$-invisible lattice points for
any fixed $b$. This work specialized to $b=1$ recovers original results from
the classical lattice point visibility setting where the lines of sight are
given by linear functions with rational slope through the origin.

Number Theory;Combinatorics