%I #8 May 05 2018 16:37:21
%S 32768,56953125,120472576
%N Least y for which x^5 + y^6 = A300567(n)^7 for some x > 1.
%C 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).
%C See the main entry A300567 for all further information.
%e 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.
%e 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.
%K nonn
%O 1,1
%A _M. F. Hasler_, Apr 23 2018
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