A308116 Sum of the perimeters of the integer-sided triangles with perimeter n whose side lengths are squarefree.

0, 0, 3, 0, 5, 6, 14, 8, 9, 0, 22, 12, 39, 28, 75, 48, 51, 36, 38, 20, 63, 66, 138, 96, 75, 52, 162, 112, 203, 210, 341, 256, 264, 204, 385, 288, 333, 228, 507, 360, 410, 252, 559, 396, 720, 552, 940, 720, 833, 600, 765, 520, 848, 756, 825, 616, 684, 580

Offset

1,3

Links

Table of n, a(n) for n=1..58.

Wikipedia, Integer Triangle

Formula

a(n) = n * A308061(n).

a(n) = 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, 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, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

Crossrefs

Cf. A008683, A308061.

Sequence in context: A307728 A263199 A052483 * A308123 A308089 A249859

Adjacent sequences: A308113 A308114 A308115 * A308117 A308118 A308119

Keyword

nonn

Author

Wesley Ivan Hurt, May 13 2019

Status

approved