A308212 - OEIS

%I #7 Jun 16 2020 14:30:24

%S 0,0,1,0,1,0,1,1,2,0,2,2,4,2,3,2,5,3,6,6,8,4,8,7,10,6,9,8,13,11,16,15,

%T 18,12,16,15,21,15,19,17,24,20,27,26,30,22,30,29,36,30,35,33,42,36,42,

%U 40,46,36,46,44,54,44,50,47,55,49,60,58,65,57,69

%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 b.

%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,i) = 1], where [] is the Iverson bracket.

%t Table[Sum[Sum[Floor[1/GCD[k, i]] Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

%Y Cf. A308211.

%K nonn

%O 1,9

%A _Wesley Ivan Hurt_, May 15 2019