  A skew morphism of a finite group $A$ is a permutation $\varphi$ of $A$
fixing the identity element and for which there is an integer-valued function
$\pi$ on $A$ such that $\varphi(ab)=\varphi(a)\varphi^{\pi(a)}(b)$ for all $a,
b \in A$. A skew morphism $\varphi$ of $A$ is smooth if the associated power
function $\pi$ is constant on the orbits of $\varphi$, that is,
$\pi(\varphi(a))\equiv\pi(a)\pmod{|\varphi|}$ for all $a\in A$. In this paper
we show that every skew morphism of a cyclic group of order $n$ is smooth if
and only if $n=2^en_1$, where $0 \le e \le 4$ and $n_1$ is an odd square-free
number. A partial solution to a similar problem on non-cyclic abelian groups is
also given.
