A300568(1) = 47775744 is the smallest z such that z^8 = x^6 + y^7 for some x, y > 1, and the smallest such y is a(1) = 12*z = 573308928. It then follows that x = (47775744^8  573308928^7)^(1/6) = 13759414272 = 288*z.
A300568(2) = 22143375000 is the second smallest z such that z^8 = x^6 + y^7 for some x, y > 1, and the smallest corresponding y is a(2) = 30*z = 664301250000. It then follows that x = (22143375000^8  664301250000^7)^(1/6) = 29893556250000 = 1350*z.
Similarly, a(3) = 30*A300568(2) = 699840000000 is the smallest y for which x = (A300568(3)^8  y^7)^(1/6) is an integer, here x = 1800*A300568(3) = 60*a(3).
