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A289219
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Areas of integer-sided triangles whose area equals 3 times their perimeter.
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7
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192, 204, 210, 216, 240, 252, 264, 270, 324, 330, 336, 378, 384, 408, 420, 456, 462, 480, 504, 522, 540, 546, 624, 690, 714, 780, 792, 840, 876, 966, 990, 1176, 1248, 1320, 1380, 1806, 2394, 2460, 3120, 4446, 8436
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OFFSET
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1,1
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COMMENTS
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There are no further terms.
For a(3)=210, there are 2 solutions (20,21,29),(17,25,28);
For a(11)=336, there are 2 solutions (14,48,50),(24,35,53);
For a(16)=456, a(22)=546, there are 2 solutions respectively too.
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LINKS
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EXAMPLE
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The areas 192,204,210,216,240, ... pertain respectively to triangles with sides (20,20,24), (17,25,26), (20,21,29), (18,24,30), (16,30,34), ..., equal 3 times their perimeter 64,68,70,72,80, ...
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MATHEMATICA
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f[a_, b_, c_] := Block[{P = Total[{a, b, c}]/2}, Sqrt[P (P - a) (P - b) (P - c)]]; Sort@ Map[f @@ # &, Select[Union@ Map[Sort, Tuples[Range@ 150, {3}]], f @@ # == 3 Total@# &] ] (* Michael De Vlieger, Jul 03 2017 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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