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%I #7 Jun 18 2020 13:44:32
%S 0,0,1,0,1,0,2,1,1,1,4,1,5,2,2,3,8,3,10,4,4,5,14,3,13,7,12,8,21,6,24,
%T 11,12,12,20,10,33,15,18,12,40,12,44,20,28,22,52,15,48,21,32,28,65,21,
%U 50,26,40,35,80,20,85,40,56,43,70,30,102,48,60,34
%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 b is coprime to n.
%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,n) = 1], where [] is the Iverson bracket.
%t Table[Sum[Sum[Floor[1/GCD[i, n]] 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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