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%I #7 Jun 16 2020 14:32:59
%S 0,0,1,0,0,0,0,0,0,0,0,5,0,0,7,7,0,15,0,17,9,9,11,53,11,21,37,60,26,
%T 103,13,68,28,74,49,193,34,115,106,210,74,291,76,227,97,214,107,464,
%U 132,345,205,414,117,592,198,488,223,454,214,1037,274,591,491
%N Sum of the largest sides of all integer-sided triangles with perimeter n whose side lengths are mutually coprime.
%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))) * [gcd(i,k) * gcd(i,n-i-k) * gcd(k,n-i-k) = 1] * (n-i-k), where [] is the Iverson Bracket.
%t Table[Sum[Sum[(n - i - k)*Floor[1/(GCD[i, k]*GCD[i, n - i - k]*GCD[k, n - i - k])]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A308223.
%K nonn
%O 1,12
%A _Wesley Ivan Hurt_, May 16 2019
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