The overpartition function modulo small powers of 2

Abstract

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