New Ramanujan-like congruences modulo powers of 2 and 3 for overpartitions

Let p¯(n) denote the number of overpartitions of n  . In recent works, Fortin, Jacob and Mathieu, and Hirschhorn and Sellers established some congruences modulo powers of 2 for p¯(n). Much less is known for powers of 3. In this paper, employing elementary generating function dissection techniques, we prove that for all nonnegative integers n,p¯(24n+19)≡0(mod27) andp¯(92n+12)≡0(mod9). Furthermore, we also derive some new congruences modulo powers of 2 for p¯(n).