%I
%S 573308928,664301250000,699840000000
%N Least y for which x^6 + y^7 = A300568(n)^8 for some x > 1.
%C The values listed here are the yvalues corresponding to the zvalues listed in A300568. The xvalues are then readily computed as (z^8  y^7)^(1/6).
%C See the main entry A300567 for all further information.
%e 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.
%e 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.
%e 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).
%Y Cf. A300564, A300565, A300566, A300567, A300568, A303265, A303266, A303267.
%K nonn
%O 1,1
%A _M. F. Hasler_, May 04 2018
