Arithmetic Properties of Overpartition Pairs into Odd Parts

In this work, we investigate various arithmetic properties of the function (pp) over bar (o)(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 (pp) over bar (o)(n). For a fixed positive integer k, we further show that (pp) over bar (o)(n) is divisible by 2(k) for almost all n. We also find several infinite families of congruences for (pp) over bar (o)(n) modulo 3 and two formulae for (pp) over bar (o)(6n+3) and (pp) over bar (o)(12n) modulo 3.