%I
%S 0,0,1,0,0,0,0,0,0,0,0,3,0,0,3,4,0,8,0,9,5,5,5,25,5,14,15,31,12,50,7,
%T 33,16,39,19,86,16,57,46,99,32,142,34,116,49,108,47,208,56,172,91,189,
%U 57,274,86,232,109,225,92,463,118,294,195,378,150,562
%N Sum of the smallest side lengths of all integersided 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((nk)/2)} sign(floor((i+k)/(nik+1))) * [gcd(i,k) * gcd(i,nik) * gcd(k,nik) = 1] * k, where [] is the Iverson Bracket.
%t Table[Sum[Sum[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. A308074.
%K nonn
%O 1,12
%A _Wesley Ivan Hurt_, May 16 2019
