A308426 Sum of the smallest 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, 4, 4, 4, 0, 8, 12, 8, 9, 12, 8, 9, 0, 8, 17, 9, 0, 24, 9, 12, 9, 24, 18, 24, 9, 44, 18, 20, 9, 48, 18, 36, 17, 77, 33, 59, 36, 83, 70, 67, 65, 123, 88, 63, 81, 111, 92, 89, 74, 169, 75, 90, 66, 154

Offset

1,12

Links

Table of n, a(n) for n=1..72.

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

Mathematica

Table[Sum[Sum[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, A308424.

Sequence in context: A360543 A236378 A341880 * A396544 A308429 A308428

Adjacent sequences: A308423 A308424 A308425 * A308427 A308428 A308429

Keyword

nonn

Author

Wesley Ivan Hurt, May 26 2019

Status

approved