On overpartition pairs into odd parts modulo powers of 2

In 2012, Lin (Electron. J. Combin. 19(2) (2012) #P17) investigated the 2 and 3-divisibility properties for pp¯o(n), the number of overpartition pairs into odd parts. Using modular forms, he proved that for a fixed positive integer k, pp¯o(n) is almost always divisible by 2k. In this paper, we prove several congruences for pp¯o(n) modulo higher powers of 2 in an elementary way.