Divisibility properties for the overpartitions into odd parts and 5-regular partitions

Abstract

In 2006, Hirschhorn and Sellers provided a full characterization of congruences modulo 8 for which denotes the number of overpartitions of n into odd parts. Recently, Merca reproved these congruences modulo 8 by using a recurrence relation for . Motivated by their works, we give a characterization of congruences modulo 16 for and deduce infinite families of congruences modulo 16 for . Furthermore, we prove two congruences modulo 8 for 5-regular partitions by using some identities due to Ramanujan.