Overpartitions and ternary quadratic forms

Let (overline{p}(n)) denote the number of overpartitions of n. Recently, Mahlburg showed that (overline{p}(n) equiv 0 pmod {64}) and Kim showed that (overline{p}(n) equiv 0 pmod {128}) for almost all integers n. In this paper, with the help of some ternary quadratic forms, we prove that (overline{p}(n) equiv 0 pmod {256}) for almost all integers n, which was conjectured by Mahlburg.