A308103 Number of scalene triangles with perimeter n whose side lengths are squarefree.

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

Offset

1,15

Links

Table of n, a(n) for n=1..78.

Wikipedia, Integer Triangle

Formula

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).

Mathematica

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}]

Crossrefs

Cf. A008683, A308061.

Sequence in context: A293513 A015738 A333815 * A368987 A115604 A128617

Adjacent sequences: A308100 A308101 A308102 * A308104 A308105 A308106

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2019

Status

approved