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A051493
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Triangles with perimeter n and relatively prime integer side lengths.
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17
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0, 0, 1, 0, 1, 0, 2, 1, 2, 1, 4, 2, 5, 2, 5, 4, 8, 4, 10, 6, 9, 6, 14, 8, 15, 9, 16, 12, 21, 11, 24, 16, 22, 16, 27, 18, 33, 20, 31, 24, 40, 23, 44, 30, 39, 30, 52, 32, 54, 35, 52, 42, 65, 38, 65, 48, 64, 49, 80, 48, 85, 56, 77, 64, 90, 58, 102, 72, 93, 69, 114, 72, 120, 81
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OFFSET
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1,7
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COMMENTS
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The triangles that meet the conditions are listed by nondecreasing n in A070110.
Without the requirement for relatively prime side lengths, this sequence becomes A005044.
Counting the triangles by longest side instead of perimeter, this sequence becomes A123323.
(End)
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LINKS
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FORMULA
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EXAMPLE
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There are 3 triangles with integer-length sides and perimeter 9: 1-4-4, 2-3-4, 3-3-3. 3-3-3 is omitted because isomorphic to 1-1-1, so a(9)=2.
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MATHEMATICA
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nmax = 100;
A005044[n_] := Quotient[n^2 + 6n Mod[n, 2] + 24, 48];
mob[m_, n_] := If[ Mod[m, n] == 0, MoebiusMu[m/n], 0];
Reap[Do[Sow[Sum[mob[n, d] A[[d]], {d, 1, n}]], {n, 1, nmax}]][[2, 1]] (* Jean-François Alcover, Oct 05 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Formula updated due to change to referenced sequence, and definition clarified by Peter Munn, Jul 26 2017
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STATUS
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approved
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