A308133 Sum of the smallest sides of all integer-sided triangles with squarefree sides and perimeter n.

0, 0, 1, 0, 1, 2, 3, 2, 3, 0, 4, 2, 6, 5, 14, 10, 13, 11, 11, 6, 13, 13, 23, 18, 15, 11, 29, 20, 29, 39, 55, 46, 54, 44, 72, 57, 70, 54, 100, 75, 91, 64, 111, 82, 139, 102, 171, 135, 172, 123, 171, 114, 176, 145, 176, 140, 163, 128, 199, 152, 204, 207, 283

Offset: 1

Author

Wesley Ivan Hurt, May 14 2019

Keywords

• nonn

Links

• Wikipedia, Integer Triangle

Crossrefs

Cf. A008683, A308116.

Programs

Mathematica

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

Formula

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