A309192 a(n) = Sum_{k=1..n} mu(k)^2 * k * floor(n/k).

1, 4, 8, 11, 17, 29, 37, 40, 44, 62, 74, 86, 100, 124, 148, 151, 169, 181, 201, 219, 251, 287, 311, 323, 329, 371, 375, 399, 429, 501, 533, 536, 584, 638, 686, 698, 736, 796, 852, 870, 912, 1008, 1052, 1088, 1112, 1184, 1232, 1244, 1252, 1270, 1342, 1384, 1438, 1450, 1522

Offset: 1

Author

Ilya Gutkovskiy, Jul 16 2019

Keywords

• nonn

Comments

Partial sums of A048250.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

Table[Sum[MoebiusMu[k]^2 k Floor[n/k], {k, 1, n}], {n, 1, 55}]
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
Accumulate[Table[Total[Select[Divisors[n], SquareFreeQ]], {n, 1, 100}]] (* Vaclav Kotesovec, Jul 16 2019 *)

Formula

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

a(n) ~ n^2/2. - Vaclav Kotesovec, Jul 16 2019