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%I #8 Jun 16 2020 13:50:07
%S 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,
%T 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,
%U 12,5,5,4,9,7,5,6,11,6,4,5,9,8,5,5,13,5
%N Number of integer-sided triangles with perimeter n whose side lengths 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), where mu is the Möbius function (A008683).
%t 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}]
%Y Cf. A008683, A308061.
%K nonn
%O 1,25
%A _Wesley Ivan Hurt_, May 26 2019