  Let $s_q(n)$ denote the sum of the digits of a number $n$ expressed in base
$q$. We study here the ratio $\frac{s_q(n^\alpha)}{s_q(n)}$ for various values
of $q$ and $\alpha$. In 1978, Kenneth B. Stolarsky showed that
$\lim\inf_{n\rightarrow\infty}\frac{s_2(n^2)}{s_2(n)}=0$ and that
$\lim\sup_{n\rightarrow\infty}\frac{s_2(n^2)}{s_2(n)}=\infty$ using an explicit
construction. We show that for $\alpha=2$ and $q\geq 2$, the above ratio can in
fact be any positive rational number. We also study what happens when $\alpha$
is a rational number that is not an integer, terminating the resulting
expression by using the floor function.
