A391773 a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 = k^3 has exactly n positive primitive integer solutions.

6, 41, 87, 219, 606, 492, 2999, 4351, 5781, 11023, 19443, 45897, 74033, 59049, 139575, 130321, 255477, 354225, 468513, 506169, 455625, 858171

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Diophantine Equation--3rd Powers.

Jaroslaw Wroblewski, Exhaustive list of solutions to (3,1,3) below 1,000,000.

Example

a(4) = 219 since 219^3 = x^3 + y^3 + z^3 has exactly 4 positive primitive integer solutions: {{50, 67, 216}, {51, 152, 190}, {67, 167, 177}, {108, 163, 170}}.

Mathematica

a[n_]:=Module[{k=1}, While[Length@Select[PowersRepresentations[k^3, 3, 3], #[[1]]>0&&GCD@@#==1&]!=n, k++]; k]; Table[a[k], {k, 4}]

Crossrefs

Cf. A316359, A377444.

Sequence in context: A354331 A000611 A043069 * A257602 A135232 A371536

Adjacent sequences: A391770 A391771 A391772 * A391774 A391775 A391776

Keyword

nonn,more

Author

Zhining Yang, Dec 19 2025

Status

approved