Abstract
Let [Formula: see text] be the number of overpartitions of [Formula: see text] into parts not divisible by [Formula: see text]. In this paper, we find infinite families of congruences modulo 4, 8 and 16 for [Formula: see text] and [Formula: see text] for any [Formula: see text]. Along the way, we obtain several Ramanujan type congruences for [Formula: see text] and [Formula: see text]. We also find infinite families of congruences modulo [Formula: see text] for [Formula: see text].
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