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 A308133 Sum of the smallest sides of all integer-sided triangles with squarefree sides and perimeter n. 0
 0, 0, 1, 0, 1, 2, 3, 2, 3, 0, 4, 2, 6, 5, 14, 10, 13, 11, 11, 6, 13, 13, 23, 18, 15, 11, 29, 20, 29, 39, 55, 46, 54, 44, 72, 57, 70, 54, 100, 75, 91, 64, 111, 82, 139, 102, 171, 135, 172, 123, 171, 114, 176, 145, 176, 140, 163, 128, 199, 152, 204, 207, 283 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 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)^2 * mu(k)^2 * mu(n-i-k)^2 * k, where mu is the Möbius function (A008683). MATHEMATICA Table[Sum[Sum[k*MoebiusMu[i]^2*MoebiusMu[k]^2*MoebiusMu[n - k - i]^2*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}] CROSSREFS Cf. A008683, A308116. Sequence in context: A354522 A059905 A295301 * A306426 A014836 A197262 Adjacent sequences: A308130 A308131 A308132 * A308134 A308135 A308136 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 14 2019 STATUS approved

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Last modified March 27 18:55 EDT 2023. Contains 361575 sequences. (Running on oeis4.)