LAUSR

Andrews defined the combinatorial objects called singular overpartitions denoted by C¯k,i(n), which counts the number of overpartitions of n in which no part is divisible by k and only parts ≡±i(modk) may be overlined. In this paper, we investigate the arithmetic properties of Andrews singular overpartition pairs. Let A¯i,jδ(n) be the number of overpartition pairs of n in which no part is divisible by δ and only parts ≡±i,±j(modδ) may be overlined. We will prove a number of Ramanujan like congruences and infinite families of congruences for A¯1,26(n) modulo 3, 9, 18 and 36, infinite families of congruences for A¯2,48(n) modulo 4 and 8, infinite families of congruences for A¯1,512(n) modulo 6 and 9.