A308103 - OEIS

%I #10 Jun 16 2020 14:24:20

%S 0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,1,0,1,0,0,1,1,3,2,0,1,2,2,4,5,7,5,3,4,

%T 6,4,4,5,7,5,4,5,7,5,9,11,13,10,9,10,9,6,10,11,10,7,6,8,9,8,12,16,17,

%U 14,13,16,18,13,22,24,27,20,19,23,24,22,29,34

%N Number of 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) = 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[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, A308061.

%K nonn

%O 1,15

%A _Wesley Ivan Hurt_, May 12 2019