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%I #8 Jun 16 2020 14:25:20
%S 0,0,1,0,1,1,1,1,1,0,1,1,2,1,3,2,3,2,2,1,2,1,2,1,2,2,4,3,3,2,5,3,6,4,
%T 6,5,5,3,6,5,7,4,6,5,7,4,8,5,7,4,8,5,9,7,10,7,10,6,9,5,7,6,10,7,8,6,7,
%U 7,9,7,12,9,13,11,14,10,14,11,15,13,18,15
%N Number of acute integer-sided triangles with perimeter n and squarefree sides.
%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)} (1-sign(floor((n-i-k)^2/(i^2+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 - k - i]^2 (1 - Sign[Floor[(n - i - k)^2/(i^2 + 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, A070093.
%K nonn
%O 1,13
%A _Wesley Ivan Hurt_, May 13 2019
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