Arithmetic properties of 3-regular partitions with distinct odd parts

Abstract

Let $$pod_3(n)$$ denote the number of 3-regular partitions of n with distinct odd parts (and even parts are unrestricted). In this article, we prove an infinite family of congruences for $$pod_3(n)$$ using the theory of Hecke eigenforms. We also study the divisibility properties of $$pod_3(n)$$ using arithmetic properties of modular forms.