The overpartition function modulo small powers of 2

In a recent paper, Fortin et al. (Jagged Partitions, arXivmath. CO/0310079, 2003) found congruences modulo powers of 2 for the values of the overpartition function (p) over bar (n) in arithmetic progressions. The moduli for these congruences ranged as high as 64. This note shows that (p) over bar (n) equivalent to 0 (mod 64) for a set of integers of arithmetic density 1. (C) 2004 Elsevier B.V. All rights reserved.