This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A303268 #10 May 08 2018 07:59:25 %S A303268 573308928,664301250000,699840000000 %N A303268 Least y for which x^6 + y^7 = A300568(n)^8 for some x > 1. %C A303268 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 A303268 See the main entry A300567 for all further information. %e A303268 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 A303268 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 A303268 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 A303268 Cf. A300564, A300565, A300566, A300567, A300568, A303265, A303266, A303267. %K A303268 nonn %O A303268 1,1 %A A303268 _M. F. Hasler_, May 04 2018