Arithmetic properties of overpartition pairs into odd parts (Q426885)

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