A169646 - OEIS

%I #14 Sep 08 2022 08:45:49

%S 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,

%T 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,

%U 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

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

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

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

%H Vincenzo Librandi, <a href="/A169646/b169646.txt">Table of n, a(n) for n = 1..3000</a>

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

%p seq(add(mobius(n*i)^2, i = 1 .. n), n = 1 .. 90); # _Ridouane Oudra_, Jul 24 2019

%t Count[#,_?SquareFreeQ]&/@Table[k*n,{n,90},{k,n}] (* _Harvey P. Dale_, Sep 05 2012 *)

%t Table[Sum[MoebiusMu[i n]^2, {i, n}], {n, 100}] (* _Vincenzo Librandi_, Jul 25 2019 *)

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

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Apr 05 2010