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 A303268 Least y for which x^6 + y^7 = A300568(n)^8 for some x > 1. 1

%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 y-values corresponding to the z-values listed in A300568. The x-values 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

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)