A343126 Numbers of the form x + y + z such that (x+y) | x*y, (y+z) | y*z, and (y+z) | x*z where x,y,z are positive integers.

6, 12, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 48, 52, 54, 55, 56, 60, 63, 66, 70, 72, 78, 80, 84, 85, 88, 90, 95, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 119, 120, 126, 130, 132, 138, 140, 143, 144, 147, 150, 152, 154, 156, 160, 162, 165, 168, 170, 171

Offset: 1

Author

Wesley Ivan Hurt, Apr 05 2021

Keywords

• nonn

Examples

			6 is in the sequence since 6 = 2 + 2 + 2, and (2+2) | 2*2 for each pair.
20 is in the sequence since 20 = 4 + 4 + 12, where (4+4) | 4*4 and (4+12) | 4*12 for the other two pairs.
21 is in the sequence since 21 = 3 + 6 + 12, where (3+6) | 3*6, (6+12) | 6*12, and (6+12) | 3*12.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..2049

Crossrefs

Cf. A005279.

Programs

Mathematica

Block[{a = {}, nn = 171}, Do[If[i > nn, Break[], Do[If[i + j > nn, Break[], Do[If[# > nn, Break[], If[And[Mod[i j, (i + j)] == 0, Mod[j k, (j + k)] == 0, Mod[i k, (j + k)] == 0], AppendTo[a, #]]] &[i + j + k], {k, j, Infinity}]], {j, i, Infinity}]], {i, Infinity}]; Union@ a] (* Michael De Vlieger, Apr 06 2021 *)