A343207 Numbers k such that there exists a unique partition of k into positive integers x,y,z such that x+y, y+z and x+z divide x*y, y*z and x*z, respectively.

6, 12, 15, 18, 20, 28, 35, 36, 40, 54, 56, 63, 70, 75, 77, 78, 88, 91, 99, 100, 102, 104, 108, 114, 117, 130, 138, 143, 153, 154, 162, 170, 174, 175, 176, 182, 184, 186, 187, 189, 190, 196, 200, 208, 209, 221, 222, 238, 245, 246, 247, 258, 261, 266, 272, 282, 286, 297

Offset: 1

Author

Jean-François Alcover, Apr 08 2021

Keywords

• nonn

Comments

A subsequence of A005279, except for terms such as 184, 261, 568, 826, 848, ..., which partition into distinct parts.

A variant of A343126.

Examples

			15 = 3+6+6 with 3+6 = 9 | 18 and 6+6 = 12 | 36.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005279, A010814, A343126.

Programs

Mathematica

sel[k_] := Select[IntegerPartitions[k, {3}], ({x, y, z} = Sort[#]; Divisible[x y, x+y] && Divisible[y z, y+z] && Divisible[x z, x+z])&];
Reap[For[k = 3, k <= 500, k++, sk = sel[k]; If[Length[sk] == 1, Print[k, " ", Sort[sk[[1]]]]; Sow[k]]]][[2, 1]]