Arithmetic Properties of Overpartition Pairs into Odd Parts

In this work, we investigate various arithmetic properties of the function ppo(n), the number of overpartition pairs of n into odd parts. We obtain a number of Ramanujan type congruences modulo small powers of 2 for ppo(n). For a fixed positive integer k, we further show that ppo(n) is divisible by 2 k for almost all n. We also find several infinite families of congruences for ppo(n) modulo 3 and two formulae for ppo(6n + 3) and ppo(12n) modulo 3.