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A308424
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Number of integer-sided triangles with perimeter n whose side lengths are nonsquarefree.
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 0, 1, 2, 1, 0, 3, 1, 2, 1, 3, 2, 3, 1, 5, 2, 2, 1, 4, 2, 3, 2, 7, 4, 5, 4, 7, 7, 6, 6, 10, 7, 5, 6, 8, 7, 6, 5, 12, 5, 5, 4, 9, 7, 5, 6, 11, 6, 4, 5, 9, 8, 5, 5, 13, 5
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OFFSET
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1,25
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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), where mu is the Möbius function (A008683).
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MATHEMATICA
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Table[Sum[Sum[(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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