Divisibility of Andrews' singular overpartitions by powers of 2 and 3

Andrews introduced the partition function (C) over bar (k,i) (n), called singular overpartition, which counts the number of overpartitions of n in which no part is divisible by k and only parts equivalent to +/- i (mod k) may be overlined. He also proved that (C) over bar (3,1)(9n + 3) and (C) over bar (3,1)(9n + 6) are divisible by 3 for n >= 0. Recently Aricheta proved that for an infinite family of k, (C) over bar (3k,k) (n) is almost always even. In this paper, we prove that for any positive integer k, (C) over bar (3,1)(n) is almost always divisible by 2(k) and 3(k)