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We say a lattice point $X=(x_1,\ldots,x_m)$ is visible from the origin, if$\gcd(x_1,...,x_m)=1$. In other word, there are no other lattice point on theline segment from the origin $O$ to $X$. From J.E. Nymann's result, we knowthat the number of lattice point from the origin in $[-r,r]^m$ is$(2r)^m/\zeta(m)+$(Error term). We showed that the exact order of the errorterm is $r^{m-1}$ for $m\ge3$.

The exact order of the number of lattice points visible from the origin