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 View the MathML sourcep¯(n) in arithmetic progressions. The moduli for these congruences ranged as high as 64. This note shows that View the MathML sourcep¯(n)≡0(mod64) for a set of integers of arithmetic density 1.