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%I #8 Jun 18 2020 13:41:22
%S 0,0,1,0,2,2,5,3,3,0,8,5,16,11,29,18,18,12,13,7,23,23,51,35,28,20,62,
%T 44,82,79,132,98,100,75,144,108,121,80,185,131,148,87,203,145,265,200,
%U 345,264,300,214,272,187,305,274,301,216,246,210,340,258,406
%N Take all the integer-sided triangles with perimeter n and squarefree sides 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))) * mu(i)^2 * mu(k)^2 * mu(n-i-k)^2 * i, where mu is the Möbius function (A008683).
%t Table[Sum[Sum[i* MoebiusMu[i]^2*MoebiusMu[k]^2*MoebiusMu[n - k - i]^2 *Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A008683, A308116.
%K nonn
%O 1,5
%A _Wesley Ivan Hurt_, May 14 2019
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