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%I #8 Jun 16 2020 14:35:31
%S 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,
%T 28,16,0,44,16,36,18,50,36,56,18,94,38,38,20,74,44,62,49,155,99,112,
%U 106,166,182,149,159,258,185,132,161,215,197,168,139,352
%N Sum of the largest side lengths of all integer-sided triangles with perimeter n whose sides are nonsquarefree.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F 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).
%t 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}]
%Y Cf. A008683, A308426.
%K nonn
%O 1,12
%A _Wesley Ivan Hurt_, May 26 2019
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