A384132 Integers k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^3, where 0 < x < y < z < w has no integer solutions.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 19, 21, 22, 25, 27, 29, 47, 58, 61, 71, 113, 121

Offset: 1

Author

Zhining Yang, May 20 2025

Keywords

• nonn
• more

Comments

Conjecture: a(27)=121 is the largest integer whose cube cannot be described as the sum of four distinct positive cubes.

Examples

			13 is not a term because 13^3 = 5^3 + 7^3 + 9^3 + 10^3 = 1^3 + 5^3 + 7^3 + 12^3.
		

Crossrefs

Cf. A003327, A383877.

Programs

Mathematica

a=Select[Range@125,Length@Select[PowersRepresentations[#^3,4,3],0<#[[1]]<#[[2]]<#[[3]]<#[[4]]&]==0&]