In an earlier paper it was argued that two sequences, denoted by {U_n} and {W_n}, constitute the sextic analogues of the well-known Lucas sequences {u_n} and {v_n}. While a number of the properties of {U_n} and {W_n} were presented previously, several arithmetic properties of these sequences were only mentioned in passing. In this paper we discuss the derived sequences {D_n} and {E_n}, where D_n = gcd(W_n - 6 Rⁿ,U_n) and E_n = gcd(W_n,U_n), in greater detail and show that they possess many number-theoretic properties analogous to those of {u_n} and {v_n}, respectively.