A308122 Sum of the perimeters of all scalene triangles with perimeter n whose side lengths are squarefree.

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, 116, 150, 217, 160, 99, 136, 210, 144, 148, 190, 273, 200, 164, 210, 301, 220, 405, 506, 611, 480, 441, 500, 459, 312, 530, 594, 550, 392, 342, 464, 531, 480, 732

Offset

1,13

Links

Table of n, a(n) for n=1..61.

Wikipedia, Integer Triangle

Formula

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

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).

Mathematica

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}]

Crossrefs

Cf. A008683, A308103.

Sequence in context: A041338 A042411 A167996 * A292116 A071870 A346544

Adjacent sequences: A308119 A308120 A308121 * A308123 A308124 A308125

Keyword

nonn

Author

Wesley Ivan Hurt, May 13 2019

Status

approved