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A309394
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Perimeters of integer-sided triangles whose side lengths are square numbers.
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1
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3, 9, 12, 19, 22, 27, 33, 34, 36, 41, 48, 51, 54, 57, 59, 66, 73, 75, 76, 77, 81, 86, 88, 97, 99, 101, 102, 107, 108, 110, 114, 121, 123, 129, 132, 134, 136, 137, 138, 144, 147, 149, 153, 162, 163, 164, 166, 170, 171, 177, 178, 179, 181, 187, 192, 194, 198
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OFFSET
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1,1
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LINKS
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MAPLE
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N:= 1000: # to get all terms <= N
S:= {}:
for a from 1 to floor(sqrt(N/3)) do
for b from a to floor(sqrt((N-a^2)/2)) do
S:= S union map(c -> a^2 + b^2 + c^2, {$b .. floor(sqrt(min(a^2+b^2-1, N-a^2-b^2)))})
od od:
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MATHEMATICA
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Flatten[Table[If[Sum[Sum[(Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[k]] - Floor[Sqrt[k - 1]]) (Floor[Sqrt[n - k - i]] - Floor[Sqrt[n - k - i - 1]])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 200}]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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