A308428 Sum of the largest 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, 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
Offset: 1
Keywords
Links
- Wikipedia, Integer Triangle
Programs
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Mathematica
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}]
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) * (n - i - k), where mu is the Möbius function (A008683).