Congruences modulo 16, 32, and 64 for Andrews's singular overpartitions

摘要

In a recent work, Andrews gave a definition of combinatorial objects which he called singular overpartitions and proved that these singular overpartitions, which depend on two parameters k and i, can be enumerated by the function which denotes the number of overpartitions of n in which no part is divisible by k and only parts may be overlined. Andrews, Chen, Hirschhorn and Sellers, and Ahmed and Baruah discovered numerous congruences modulo 2, 3, 4, 8, and 9 for . In this paper, we prove a number of congruences modulo 16, 32, and 64 for (C) over bar3,1 (n).