Some Properties of Overpartitions into Nonmultiples of Two Integers

We consider properties of overpartitions that are simultaneously {\ell}-regular and μ-regular, where {\ell} and μ are positive relatively prime integers. We prove a seven-way combinatorial identity related to these overpartitions. We also prove several congruence properties satisfied by this class of partitions (and a further related class) using both generating functions and modular forms with Radu’s Algorithm.