%I
%S 0,0,1,0,0,0,0,0,0,0,0,4,0,0,5,5,0,13,0,14,7,8,7,42,9,17,29,49,20,87,
%T 11,59,22,57,37,153,24,94,82,171,58,239,62,185,79,184,81,384,106,283,
%U 163,333,91,484,156,400,181,365,166,840,218,479,385,660,280
%N Take the integersided triangles with perimeter n and mutually coprime 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((nk)/2)} sign(floor((i+k)/(nik+1))) * [gcd(i,k) * gcd(i,nik) * gcd(k,nik) = 1] * i, where [] is the Iverson Bracket.
%t Table[Sum[Sum[i*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. A308224.
%K nonn
%O 1,12
%A _Wesley Ivan Hurt_, May 16 2019
