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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, 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
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
Sequence in context: A241570 A083344 A294889 * A063863 A236238 A340362
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 26 2019
STATUS
approved