A346594 Numbers k such that (65*k)^2 can be represented in exactly 4 ways as the sum of a positive square and a positive fourth power.

7225, 28900, 34225, 65025, 115600, 136900, 180625, 235225, 260100, 308025, 354025, 395641, 462400, 547600, 585225, 722500, 835635, 855625, 874225, 940900, 1040400, 1221025, 1232100, 1416100, 1422798, 1582564, 1625625, 1677025, 1849600, 2088025, 2117025, 2190400

Offset: 1

Author

Hugo Pfoertner, Jul 28 2021

Keywords

• nonn

Comments

All terms multiplied by 65 are in A346110. It is unknown whether A346110 contains terms not of this form.

From Karl-Heinz Hofmann, Aug 28 2021: (Start)

A346110(44,46,53,95,97) are not divisible by 65 (5*13), but these few terms are all divisible by 145 (5*29). For further information about divisibility, see the links to A346110 below. (End)

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..208
• Karl-Heinz Hofmann, All valid {z,x1,y1,x2,y2,x3,y3,x4,y4} sets up to 10^9
• Karl-Heinz Hofmann, A 3D Animation of the solutions up to 10^9

Crossrefs

Cf. A346110.