A308426 Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose sides are nonsquarefree.
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 8, 12, 8, 9, 12, 8, 9, 0, 8, 17, 9, 0, 24, 9, 12, 9, 24, 18, 24, 9, 44, 18, 20, 9, 48, 18, 36, 17, 77, 33, 59, 36, 83, 70, 67, 65, 123, 88, 63, 81, 111, 92, 89, 74, 169, 75, 90, 66, 154
Offset: 1
Keywords
Links
- Wikipedia, Integer Triangle
Programs
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Mathematica
Table[Sum[Sum[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}]
Formula
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) * k, where mu is the Möbius function (A008683).