A303265 Least y for which x^3 + y^4 = z^5 for some x > 1 and z = A300565(n).

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

Offset: 1

Author

M. F. Hasler, Apr 23 2018

Keywords

• nonn
• more

Comments

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).

See the main entry A300565 for all further information.

Examples

			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.
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.
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.