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%I #8 Jun 18 2020 13:58:09
%S 0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,8,8,9,0,8,17,9,9,20,9,9,0,12,
%T 21,9,0,40,12,28,12,46,28,46,16,82,34,34,18,70,36,52,36,132,80,99,78,
%U 143,147,132,130,219,154,115,136,186,166,139,122,295,126
%N Take all the integer-sided triangles with perimeter n and nonsquarefree side lengths a, b and c such that a <= b <= c. a(n) is the sum of all the b's.
%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) * i, where mu is the Möbius function (A008683).
%t Table[Sum[Sum[i (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, A308428.
%K nonn
%O 1,12
%A _Wesley Ivan Hurt_, May 26 2019
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