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%I #19 Jun 16 2020 13:02:32
%S 0,0,1,0,1,1,2,1,1,0,2,1,3,2,5,3,3,2,2,1,3,3,6,4,3,2,6,4,7,7,11,8,8,6,
%T 11,8,9,6,13,9,10,6,13,9,16,12,20,15,17,12,15,10,16,14,15,11,12,10,16,
%U 12,18,18,25,19,21,19,26,19,29,27,35,27,29,27
%N Number of integer-sided triangles with perimeter n whose side lengths are squarefree.
%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))) * mu(i)^2 * mu(k)^2 * mu(n-i-k)^2, where mu is the Möbius function (A008683).
%t Table[Sum[Sum[MoebiusMu[i]^2*MoebiusMu[k]^2*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. A005044, A008683.
%K nonn,easy
%O 1,7
%A _Wesley Ivan Hurt_, May 10 2019
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