A308428 Sum of the largest side lengths of all integer-sided triangles with perimeter n whose sides are nonsquarefree.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 0, 8, 21, 9, 9, 24, 12, 12, 0, 12, 28, 16, 0, 44, 16, 36, 18, 50, 36, 56, 18, 94, 38, 38, 20, 74, 44, 62, 49, 155, 99, 112, 106, 166, 182, 149, 159, 258, 185, 132, 161, 215, 197, 168, 139, 352

Offset

1,12

Links

Table of n, a(n) for n=1..68.

Wikipedia, Integer Triangle

Formula

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

Mathematica

Table[Sum[Sum[(n - i - k) (1 - MoebiusMu[i]^2)*(1 - MoebiusMu[k]^2)*(1 - 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, A308426.

Sequence in context: A341880 A308426 A308429 * A308276 A340977 A180989

Adjacent sequences: A308425 A308426 A308427 * A308429 A308430 A308431

Keyword

nonn

Author

Wesley Ivan Hurt, May 26 2019

Status

approved