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 A334361 Number of r X s rectangles with squarefree side lengths such that r < s, r + s = 2n and r | s. 1
 0, 1, 1, 2, 0, 2, 1, 2, 2, 2, 1, 3, 0, 2, 1, 2, 1, 4, 1, 4, 3, 3, 0, 3, 0, 2, 2, 2, 1, 4, 1, 1, 2, 3, 2, 4, 1, 2, 2, 3, 0, 5, 1, 4, 3, 2, 1, 3, 2, 1, 2, 4, 1, 4, 2, 3, 3, 3, 0, 6, 0, 3, 3, 1, 1, 4, 1, 3, 2, 5, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 1, 5, 1, 2, 2, 3, 1, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS FORMULA a(n) = Sum_{i=1..n-1} (1 - ceiling((2*n-i)/i) + floor((2*n-i)/i)) * mu(i)^2 * mu(2*n-i)^2, where mu is the Möbius function (A008683). EXAMPLE a(12) = 3; 2*12 = 24 has 3 rectangles with squarefree side lengths, 1 X 23, 2 X 22 and 3 X 21 such that 1 | 23, 2 | 22 and 3 | 21. MATHEMATICA Table[Sum[MoebiusMu[i]^2 MoebiusMu[2 n - i]^2 (1 - Ceiling[(2 n - i)/i] + Floor[(2 n - i)/i]), {i, n - 1}], {n, 100}] CROSSREFS Cf. A008683, A327567. Sequence in context: A319514 A141454 A301564 * A219791 A029345 A153149 Adjacent sequences:  A334358 A334359 A334360 * A334362 A334363 A334364 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Apr 24 2020 STATUS approved

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Last modified April 19 15:00 EDT 2021. Contains 343116 sequences. (Running on oeis4.)