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a(n) = Sum_{k=1..n} mu(k)^2 * k * floor(n/k).
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%I #9 Jul 16 2019 08:33:12

%S 1,4,8,11,17,29,37,40,44,62,74,86,100,124,148,151,169,181,201,219,251,

%T 287,311,323,329,371,375,399,429,501,533,536,584,638,686,698,736,796,

%U 852,870,912,1008,1052,1088,1112,1184,1232,1244,1252,1270,1342,1384,1438,1450,1522

%N a(n) = Sum_{k=1..n} mu(k)^2 * k * floor(n/k).

%C Partial sums of A048250.

%H Vaclav Kotesovec, <a href="/A309192/b309192.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k)^2 * k * x^k/(1 - x^k).

%F a(n) ~ n^2/2. - _Vaclav Kotesovec_, Jul 16 2019

%t Table[Sum[MoebiusMu[k]^2 k Floor[n/k], {k, 1, n}], {n, 1, 55}]

%t nmax = 55; CoefficientList[Series[1/(1 - x) Sum[MoebiusMu[k]^2 k x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%t Accumulate[Table[Total[Select[Divisors[n], SquareFreeQ]], {n, 1, 100}]] (* _Vaclav Kotesovec_, Jul 16 2019 *)

%Y Cf. A008683, A024916, A024924, A048250, A064608, A275205.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Jul 16 2019