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A308116
Sum of the perimeters of the integer-sided triangles with perimeter n whose side lengths are squarefree.
3
0, 0, 3, 0, 5, 6, 14, 8, 9, 0, 22, 12, 39, 28, 75, 48, 51, 36, 38, 20, 63, 66, 138, 96, 75, 52, 162, 112, 203, 210, 341, 256, 264, 204, 385, 288, 333, 228, 507, 360, 410, 252, 559, 396, 720, 552, 940, 720, 833, 600, 765, 520, 848, 756, 825, 616, 684, 580
OFFSET
1,3
FORMULA
a(n) = n * A308061(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))) * mu(i)^2 * mu(k)^2 * mu(n-i-k)^2, where mu is the Möbius function (A008683).
MATHEMATICA
Table[n*Sum[Sum[MoebiusMu[i]^2*MoebiusMu[k]^2*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
Sequence in context: A263199 A052483 A373775 * A308123 A308089 A249859
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 13 2019
STATUS
approved