Congruences modulo 9 and 27 for overpartitions

Let denote the number of overpartitions of n. Fortin et al. and Hirschhorn and Sellers established some congruences modulo powers of 2 for . Recently, Xia and Yao found several congruences modulo powers of 2 and 3. In particular, they proved that and . In this paper, we generalize the two congruences and establish several new infinite families of congruences modulo 9 and 27 for . Furthermore, we prove some strange congruences modulo 9 and 27 for by employing some results due to Cooper et al. For example, we prove that for , and . We also present two conjectures on congruences for p(n).