A308229 - OEIS

%I #8 Jun 18 2020 13:48:52

%S 0,0,3,0,0,0,0,0,0,0,0,12,0,0,15,16,0,36,0,40,21,22,23,120,25,52,81,

%T 140,58,240,31,160,66,170,105,432,74,266,234,480,164,672,172,528,225,

%U 506,235,1056,294,800,459,936,265,1350,440,1120,513,1044,472,2340

%N Sum of the perimeters of all 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) = n * A308074(n).

%F a(n) = 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], where [] is the Iverson Bracket.

%t Table[n*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}]

%Y Cf. A308074.

%K nonn

%O 1,3

%A _Wesley Ivan Hurt_, May 16 2019