On some congruences for (j,k)-regular overpartitions

Abstract

Let p_j,k(n) denote the number of (j, k)-regular overpartitions of n in which none of the parts congruent to j (mod k). In this paper, we obtained infinitely many families of congruences modulo powers of 2 for p_3,6(n), p_{5, 10}(n) and p_{9, 18}(n). For example, for all n ≥ 0 and α, β ≥ 0,
p_{9, 18}(3^4α+1 ∙ 5^2β+1(24 (5n+i)+23)) ≡ 0 (mod 64) where i=0, 1, 2, 4.