Congruences for Andrews' Singular Overpartitions

Many authors have found congruences and infinite families of congruences modulo 2, 3, 4, 18, and 36 for Andrews' defined combinatorial objects, called singular overpartitions, denoted by View the MathML source, which count the number of overpartitions of n in which no part is divisible by δ and only parts View the MathML source may be overlined. In this paper, we find congruences for View the MathML source modulo 4, 6, 12, 16, 18, and 72; infinite families of congruences modulo 12, 18, 48, and 72 for View the MathML source; and infinite families of congruences modulo 2 for View the MathML source, View the MathML source and View the MathML source. In addition, we find congruences for View the MathML source which represents the number of overpartitions where the parts are not multiples of 5