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%I #17 Jan 05 2024 01:43:13
%S 0,2,3,12,10,24,21,48,45,80,66,168,143,154,120,272,306,288,247,640,
%T 525,594,437,936,800,1014,945,1624,1160,1410,992,1952,1551,2210,1435,
%U 3348,2146,2546,2106,3800,2993,3360,3827,5720,4905,4324,4089,6816,5390,5300
%N Total area of all rectangles with dimensions p and p + q such that p and q are both squarefree, n = p + q and p <= q.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = n * Sum_{i=1..floor(n/2)} i * mu(i)^2 * mu(n-i)^2, where mu is the Möbius function (A008683).
%F a(n) = n * A261985(n). - _Wesley Ivan Hurt_, Jan 05 2024
%t Table[n*Sum[i*MoebiusMu[i]^2 MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n,80}]
%o (Magma) [0] cat [&+[n*k*MoebiusMu(k)^2*MoebiusMu(n-k)^2: k in [1..Floor(n/2)]]: n in [2..60]]; // _Vincenzo Librandi_, Apr 21 2018
%o (PARI) a(n) = n * sum(i=1, n\2, i * moebius(i)^2 * moebius(n-i)^2); \\ _Michel Marcus_, Apr 21 2018
%Y Cf. A008683, A261985.
%K nonn,easy
%O 1,2
%A _Wesley Ivan Hurt_, Apr 19 2018
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