A308429 Take all the integer-sided triangles with perimeter n and nonsquarefree side lengths a, b and c such that a <= b <= c. a(n) is the sum of all the b's.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 8, 9, 0, 8, 17, 9, 9, 20, 9, 9, 0, 12, 21, 9, 0, 40, 12, 28, 12, 46, 28, 46, 16, 82, 34, 34, 18, 70, 36, 52, 36, 132, 80, 99, 78, 143, 147, 132, 130, 219, 154, 115, 136, 186, 166, 139, 122, 295, 126

Offset

1,12

Links

Table of n, a(n) for n=1..69.

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) * i, where mu is the Möbius function (A008683).

Mathematica

Table[Sum[Sum[i (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, A308428.

Sequence in context: A236378 A341880 A308426 * A308428 A308276 A340977

Adjacent sequences: A308426 A308427 A308428 * A308430 A308431 A308432

Keyword

nonn

Author

Wesley Ivan Hurt, May 26 2019

Status

approved