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 A308061 Number of integer-sided triangles with perimeter n whose side lengths are squarefree. 6
 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 2, 1, 3, 2, 5, 3, 3, 2, 2, 1, 3, 3, 6, 4, 3, 2, 6, 4, 7, 7, 11, 8, 8, 6, 11, 8, 9, 6, 13, 9, 10, 6, 13, 9, 16, 12, 20, 15, 17, 12, 15, 10, 16, 14, 15, 11, 12, 10, 16, 12, 18, 18, 25, 19, 21, 19, 26, 19, 29, 27, 35, 27, 29, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS Table of n, a(n) for n=1..74. 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)^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, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}] CROSSREFS Cf. A005044, A008683. Sequence in context: A071462 A101979 A369241 * A339448 A060582 A060450 Adjacent sequences: A308058 A308059 A308060 * A308062 A308063 A308064 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, May 10 2019 STATUS approved

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Last modified September 8 19:48 EDT 2024. Contains 375759 sequences. (Running on oeis4.)