A303265 - OEIS

%I #5 Apr 25 2018 14:00:58

%S 64,625,11664,19208,23328,134456,331776,331776,531441,923521

%N Least y for which x^3 + y^4 = z^5 for some x > 1 and z = A300565(n).

%C The values listed here are the y-values corresponding to the z-values listed in A300565. The x-values are then readily computed as (z^6 - y^5)^(1/4).

%C See the main entry A300565 for all further information.

%e A300565(1) = 32 is the smallest z such that z^5 = x^3 + y^4 for some x, y > 1, and the smallest such y is a(1) = 64. It then follows that x = (32^5 - 64^4)^(1/3) = (2^24)^(1/3) = 256.

%e A300565(2) = 250 is the second smallest z such that z^5 = x^3 + y^4 for some x, y > 1, and the smallest corresponding y is a(2) = 625. It then follows that x = (250^5 - 625^4)^(1/3) = 9375.

%e A300565(3) = 1944 is the next larger z such that z^5 = x^3 + y^4 for some x, y > 1, and the smallest corresponding y is a(2) = 11664. It then follows that x = (1944^5 - 11664^4)^(1/3) = 209952.

%K nonn,more

%O 1,1

%A _M. F. Hasler_, Apr 23 2018