Abstract
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 C‾δ,i(n), which count the number of overpartitions of n in which no part is divisible by δ and only parts ≡±i(modδ) may be overlined. In this paper, we find congruences for C‾3,1(n) modulo 4, 6, 12, 16, 18, and 72; infinite families of congruences modulo 12, 18, 48, and 72 for C‾3,1(n); and infinite families of congruences modulo 2 for C‾16,4(n), C‾21,7(n) and C‾28,7(n). In addition, we find congruences for A‾5(n) which represents the number of overpartitions where the parts are not multiples of 5.
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