A308425 Sum of the perimeters of all integer-sided triangles with perimeter n whose side lengths are nonsquarefree.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 20, 21, 22, 0, 24, 50, 26, 27, 56, 29, 30, 0, 32, 66, 34, 0, 108, 37, 76, 39, 120, 82, 126, 43, 220, 90, 92, 47, 192, 98, 150, 102, 364, 212, 270, 220, 392, 399, 348, 354, 600, 427, 310, 378, 512, 455

Offset

1,12

Links

Table of n, a(n) for n=1..65.

Wikipedia, Integer Triangle

Formula

a(n) = n * A308424(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))) * (1 - mu(i)^2) * (1 - mu(k)^2) * (1 - mu(n-i-k)^2), where mu is the Möbius function (A008683).

Mathematica

Table[n*Sum[Sum[(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: A241570 A083344 A294889 * A063863 A236238 A340362

Adjacent sequences: A308422 A308423 A308424 * A308426 A308427 A308428

Keyword

nonn

Author

Wesley Ivan Hurt, May 26 2019

Status

approved