This is the list of y values corresponding to the solutions z of z^7 = y^6 + x^5 listed in A300567. The x values are then readily computed as (z^7 - y^6)^(1/5).

See the main entry A300567 for all further information.

A300567(1) = 8192 is the smallest z such that z^7 = x^5 + y^6 for some x,y > 1, and the smallest such y is a(1) = 32768. It then follows that x = (8192^7 - 32768^6)^(1/5) = 262144.

A300567(2) = 7593750 is the second smallest z such that z^7 = x^5 + y^6 for some x, y > 1, and the smallest corresponding y is a(2) = 56953125. It then follows that x = (7593750^7 - 56953125^6)^(1/5) = 4271484375.