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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.
5
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 05 2021
STATUS
approved