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%I #5 Feb 01 2021 18:36:14
%S 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,
%T 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,
%U 2,5,1,4,1,2,2,3,1,4,1,3,2,2,1,5,1,2,2,3,1,6
%N Number of r X s rectangles with squarefree side lengths such that r < s, r + s = 2n and r | s.
%F 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).
%e 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.
%t 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}]
%Y Cf. A008683, A327567.
%K nonn,easy
%O 1,4
%A _Wesley Ivan Hurt_, Apr 24 2020
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