A308122 - OEIS

%I #8 Jun 18 2020 13:39:51

%S 0,0,0,0,0,0,0,0,0,0,0,0,13,14,30,16,0,18,0,0,21,22,69,48,0,26,54,56,

%T 116,150,217,160,99,136,210,144,148,190,273,200,164,210,301,220,405,

%U 506,611,480,441,500,459,312,530,594,550,392,342,464,531,480,732

%N Sum of the perimeters of all scalene triangles with perimeter n whose side lengths are squarefree.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%F a(n) = n * A308103(n).

%F a(n) = n * Sum_{k=1..floor((n-1)/3)} Sum_{i=k+1..floor((n-k-1)/2)} sign(floor((i+k)/(n-i-k+1))) * mu(i)^2 * mu(k)^2 * mu(n-i-k)^2, where mu is the Möbius function (A008683).

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

%Y Cf. A008683, A308103.

%K nonn

%O 1,13

%A _Wesley Ivan Hurt_, May 13 2019