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A308133
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Sum of the smallest sides of all integer-sided triangles with squarefree sides and perimeter n.
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0
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0, 0, 1, 0, 1, 2, 3, 2, 3, 0, 4, 2, 6, 5, 14, 10, 13, 11, 11, 6, 13, 13, 23, 18, 15, 11, 29, 20, 29, 39, 55, 46, 54, 44, 72, 57, 70, 54, 100, 75, 91, 64, 111, 82, 139, 102, 171, 135, 172, 123, 171, 114, 176, 145, 176, 140, 163, 128, 199, 152, 204, 207, 283
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OFFSET
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1,6
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LINKS
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Table of n, a(n) for n=1..63.
Wikipedia, Integer Triangle
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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))) * mu(i)^2 * mu(k)^2 * mu(n-i-k)^2 * k, where mu is the Möbius function (A008683).
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MATHEMATICA
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Table[Sum[Sum[k*MoebiusMu[i]^2*MoebiusMu[k]^2*MoebiusMu[n - k - i]^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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Cf. A008683, A308116.
Sequence in context: A354522 A059905 A295301 * A306426 A014836 A197262
Adjacent sequences: A308130 A308131 A308132 * A308134 A308135 A308136
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KEYWORD
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nonn
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AUTHOR
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Wesley Ivan Hurt, May 14 2019
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STATUS
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approved
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