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A308428
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Sum of the largest side lengths of all integer-sided triangles with perimeter n whose sides are nonsquarefree.
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1
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 0, 8, 21, 9, 9, 24, 12, 12, 0, 12, 28, 16, 0, 44, 16, 36, 18, 50, 36, 56, 18, 94, 38, 38, 20, 74, 44, 62, 49, 155, 99, 112, 106, 166, 182, 149, 159, 258, 185, 132, 161, 215, 197, 168, 139, 352
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OFFSET
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1,12
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * (1 - mu(i)^2) * (1 - mu(k)^2) * (1 - mu(n-i-k)^2) * (n - i - k), where mu is the Möbius function (A008683).
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MATHEMATICA
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Table[Sum[Sum[(n - i - k) (1 - MoebiusMu[i]^2)*(1 - MoebiusMu[k]^2)*(1 - MoebiusMu[n - i - k]^2)*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
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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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