  The Huneke-Wiegand conjecture has prompted much recent research in
Commutative Algebra. In studying this conjecture for certain classes of rings,
Garc\'ia-S\'anchez and Leamer construct a monoid S_\Gamma^s whose elements
correspond to arithmetic sequences in a numerical monoid \Gamma of step size s.
These monoids, which we call Leamer monoids, possess a very interesting
factorization theory that is significantly different from the numerical monoids
from which they are derived. In this paper, we offer much of the foundational
theory of Leamer monoids, including an analysis of their atomic structure, and
investigate certain factorization invariants. Furthermore, when S_\Gamma^s is
an arithmetical Leamer monoid, we give an exact description of its atoms and
use this to provide explicit formulae for its Delta set and catenary degree.
