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%I #7 Jun 16 2020 14:30:00
%S 0,0,1,0,1,0,2,1,1,1,4,2,3,1,4,4,6,4,8,5,5,4,10,7,10,8,14,12,15,10,15,
%T 11,13,12,20,17,21,16,24,22,27,22,30,24,27,25,37,30,34,28,37,34,40,32,
%U 42,38,42,39,54,46,53,45,59,56,63,57,69,60,65,60,74
%N Number of integer-sided triangles with perimeter n and sides a, b and c such that a <= b <= c and the length of side a is coprime to c.
%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(k,n-i-k) = 1], where [] is the Iverson bracket.
%t Table[Sum[Sum[Floor[1/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. A308209.
%K nonn
%O 1,7
%A _Wesley Ivan Hurt_, May 15 2019
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