  This note is concerned with series of the forms $\sum f(a^n)$ and $\sum
f(n^{-a})$ where f(a) possesses a Mellin transform and $a > 1$ or $a<0$
respectively. Integral representations are derived and used to transform these
series in several ways yielding a selection of interesting integral evaluations
involving Riemann's function $\zeta(s)$, limits and series representations
containing hyperpowers. A number of examples of such sums are provided, each of
which is investigated for possible new structure. In one case, we obtain a
generalization of Riemann's classic relationship among the Zeta, Gamma and
Jacobi Theta functions.
