A169646 Number of squarefree numbers of form k*n, 1 <= k <= n.

1, 1, 2, 0, 3, 2, 5, 0, 0, 3, 7, 0, 8, 5, 6, 0, 11, 0, 12, 0, 8, 9, 15, 0, 0, 10, 0, 0, 17, 8, 19, 0, 13, 13, 15, 0, 23, 15, 17, 0, 26, 11, 28, 0, 0, 18, 30, 0, 0, 0, 21, 0, 32, 0, 25, 0, 23, 23, 36, 0, 37, 25, 0, 0, 30, 18, 41, 0, 29, 22, 44, 0, 45, 30, 0, 0, 36, 22, 49, 0, 0, 32, 51, 0, 41, 34

Offset

1,3

Comments

a(n) = A008966(n)*A073311(n);

a(A000040(n)) = A112929(n).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Formula

a(n) = Sum_{i=1..n} mu(n*i)^2, where mu is the Moebius function (A008683). - Ridouane Oudra, Jul 24 2019

Maple

seq(add(mobius(n*i)^2, i = 1 .. n), n = 1 .. 90); # Ridouane Oudra, Jul 24 2019

Mathematica

Count[#, _?SquareFreeQ]&/@Table[k*n, {n, 90}, {k, n}] (* Harvey P. Dale, Sep 05 2012 *)
Table[Sum[MoebiusMu[i n]^2, {i, n}], {n, 100}] (* Vincenzo Librandi, Jul 25 2019 *)

Prog

(Magma) [&+[MoebiusMu(k*n)^2: k in [1..n]]: n in [1..80]]; // Vincenzo Librandi, Jul 25 2019

Crossrefs

Sequence in context: A008819 A279591 A279675 * A349125 A231117 A021496

Adjacent sequences: A169643 A169644 A169645 * A169647 A169648 A169649

Keyword

nonn

Author

Reinhard Zumkeller, Apr 05 2010

Status

approved