  In this note we study the Reidemeister spectrum for metabelian groups of the
form ${\mathbb Q}^n\rtimes \mathbb Z$ and ${\mathbb Z[1/p]}^n\rtimes \mathbb
Z$. Particular attention is given to the $R_{\infty}$ property of a subfamily
of these groups. We also define a Nielsen spectrum of a space and discuss some
examples.
