A308223 - OEIS

%I #7 Jun 16 2020 14:32:06

%S 0,0,1,0,0,0,0,0,0,0,0,3,0,0,3,4,0,8,0,9,5,5,5,25,5,14,15,31,12,50,7,

%T 33,16,39,19,86,16,57,46,99,32,142,34,116,49,108,47,208,56,172,91,189,

%U 57,274,86,232,109,225,92,463,118,294,195,378,150,562

%N Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose side lengths are mutually coprime.

%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,k) * gcd(i,n-i-k) * gcd(k,n-i-k) = 1] * k, where [] is the Iverson Bracket.

%t Table[Sum[Sum[k*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. A308074.

%K nonn

%O 1,12

%A _Wesley Ivan Hurt_, May 16 2019