A070544 - OEIS

%I #11 Jan 08 2022 23:49:50

%S 0,1,1,3,2,3,3,5,6,6,6,8,7,7,7,9,9,11,11,13,13,14,13,15,15,15,16,17,

%T 17,18,18,19,19,20,20,22,22,22,22,24,23,24,24,26,27,27,27,29,30,30,30,

%U 32,32,34,34,36,36,37,36,38,37,38,38,39,39,40,40,41,41,42,42,44,44,44,45

%N Number of squarefree numbers s such that n < s < 2n.

%C Lim_{n -> infinity} a(n)/n = 6/Pi^2.

%F From _Wesley Ivan Hurt_, Jan 08 2022: (Start)

%F a(n) = Sum_{k=1..n-1} mu(2n-k)^2.

%F a(n) = Sum_{k=n+1..2n-1} mu(k)^2.

%F a(n) = Sum_{k=(n^2-n+2)/2..(n^2+n-2)/2} mu(A128076(k))^2. (End)

%t Table[Count[Range[n+1,2n-1],_?SquareFreeQ],{n,80}] (* _Harvey P. Dale_, Mar 23 2019 *)

%o (PARI) for(n=1,100,print1(sum(i=n+1,2*n-1,issquarefree(i)),","))

%Y Cf. A008966, A128076.

%K easy,nonn

%O 1,4

%A _Benoit Cloitre_, May 02 2002