  The power sum $1^n + 2^n + \cdots + x^n$ has been of interest to
mathematicians since classical times. Johann Faulhaber, Jacob Bernoulli, and
others who followed expressed power sums as polynomials in $x$ of degree $n+1$
with rational coefficients. Here we consider the denominators of these
polynomials, and prove some of their properties. A remarkable one is that such
a denominator equals $n+1$ times the squarefree product of certain primes $p$
obeying the condition that the sum of the base-$p$ digits of $n+1$ is at least
$p$. As an application, we derive a squarefree product formula for the
denominators of the Bernoulli polynomials.
