%I
%S 0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,2,0,2,1,1,1,5,1,2,3,5,2,8,1,5,2,5,
%T 3,12,2,7,6,12,4,16,4,12,5,11,5,22,6,16,9,18,5,25,8,20,9,18,8,39,10,
%U 22,17,29,12,42,11,32,15,37,11,49,9,32,22,41,15
%N Number of integersided triangles with perimeter n whose side lengths are mutually coprime.
%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], where [] is the Iverson bracket.
%t Table[Sum[Sum[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}]
%K nonn
%O 1,18
%A _Wesley Ivan Hurt_, May 11 2019
