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A335621 Number of integer-sided triangles with perimeter n such that the sum of each pair of side lengths is squarefree. 1
0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 1, 2, 3, 4, 2, 3, 2, 2, 4, 5, 4, 4, 3, 3, 3, 3, 5, 5, 4, 4, 6, 8, 5, 8, 8, 12, 7, 12, 7, 10, 6, 10, 10, 15, 14, 20, 14, 18, 17, 21, 20, 25, 20, 23, 18, 19, 16, 20, 22, 24, 21, 25, 21, 22, 20, 22, 23, 28, 22, 28, 22, 24, 20, 23, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
LINKS
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))) * mu(i+k)^2 * mu(n-i)^2 * mu(n-k)^2, where mu is the Möbius function (A008683).
MATHEMATICA
Table[Sum[Sum[MoebiusMu[i + k]^2*MoebiusMu[n - i]^2*MoebiusMu[n - 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, A308061 (each side length is squarefree).
Cf. A335621 (averages of each pair of side lengths is prime).
Sequence in context: A086831 A191340 A211229 * A316675 A111405 A089053
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 02 2020
STATUS
approved

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Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)