  We pose a conjecture on the K-theory of the self-similar $k$-graph C*-algebra
of a standard product of odometers. We generalize the C*-algebra
$\mathcal{Q}_S$ to any subset of $\mathbb{N}^\times \setminus \{1\}$ and then
realize it as the self-similar $k$-graph C*-algebra of a standard product of
odometers.
