A343126 - OEIS

%I #13 Apr 09 2021 09:40:29

%S 6,12,18,20,21,24,28,30,35,36,40,42,48,52,54,55,56,60,63,66,70,72,78,

%T 80,84,85,88,90,95,96,99,100,102,104,105,108,110,112,114,117,119,120,

%U 126,130,132,138,140,143,144,147,150,152,154,156,160,162,165,168,170,171

%N 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.

%H Michael De Vlieger, <a href="/A343126/b343126.txt">Table of n, a(n) for n = 1..2049</a>

%e 6 is in the sequence since 6 = 2 + 2 + 2, and (2+2) | 2*2 for each pair.

%e 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.

%e 21 is in the sequence since 21 = 3 + 6 + 12, where (3+6) | 3*6, (6+12) | 6*12, and (6+12) | 3*12.

%t 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 *)

%Y Cf. A005279.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Apr 05 2021