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A308103 Number of scalene triangles with perimeter n whose side lengths are squarefree. 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 0, 1, 1, 3, 2, 0, 1, 2, 2, 4, 5, 7, 5, 3, 4, 6, 4, 4, 5, 7, 5, 4, 5, 7, 5, 9, 11, 13, 10, 9, 10, 9, 6, 10, 11, 10, 7, 6, 8, 9, 8, 12, 16, 17, 14, 13, 16, 18, 13, 22, 24, 27, 20, 19, 23, 24, 22, 29, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,15

LINKS

Table of n, a(n) for n=1..78.

FORMULA

a(n) = Sum_{k=1..floor((n-1)/3)} Sum_{i=k+1..floor((n-k-1)/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[Sum[Sum[MoebiusMu[i]^2*MoebiusMu[k]^2*MoebiusMu[n - i - k]^2*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k + 1, Floor[(n - k - 1)/2]}], {k, Floor[(n - 1)/3]}], {n, 100}]

CROSSREFS

Cf. A008683, A308061.

Sequence in context: A325699 A293513 A015738 * A115604 A128617 A116488

Adjacent sequences:  A308100 A308101 A308102 * A308104 A308105 A308106

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 12 2019

STATUS

approved

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)