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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A005279.

Sequence in context: A315721 A037363 A315722 * A049094 A105935 A105289

Adjacent sequences: A343123 A343124 A343125 * A343127 A343128 A343129

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 05 2021

Status

approved