A077641 - OEIS

%I #18 Jul 29 2017 20:15:08

%S 1,2,2,3,3,4,4,5,6,7,7,8,8,8,8,9,10,11,12,13,14,15,14,15,15,16,16,17,

%T 18,19,19,19,20,21,21,22,23,23,23,24,24,25,25,26,27,28,28,29,30,30,31,

%U 32,33,34,35,36,37,38,37,38,38,39,38,39,40,41,41,41,42,43,43,44,45,45

%N Number of squarefree integers in closed interval [n, 2n-1], i.e., among n consecutive numbers beginning with n.

%F a(n) = Sum_{j=0..n-1} abs(mu(n+j)).

%F a(1) = 1; a(n + 1) = a(n) - issquarefree(n) + issquarefree(2n-2) + issquarefree(2n-1) for n > 0. - _David A. Corneth_, May 20 2016

%e n=10: among numbers {10,...,19} seven are squarefree [10,11,13,14,15,17,19], so a(10)=7.

%t Table[Apply[Plus, Table[Abs[MoebiusMu[w+j]], {j, 0, w-1}]], {w, 1, 128}]

%t Table[Count[Range[n,2n-1],_?SquareFreeQ],{n,80}] (* _Harvey P. Dale_, Oct 27 2013 *)

%t Module[{nn=80,sf},sf=Table[If[SquareFreeQ[n],1,0],{n,2nn}];Table[Total[ Take[ sf,{i,2i-1}]],{i,nn}]] (* _Harvey P. Dale_, May 20 2016 *)

%Y Cf. A005117.

%K nonn

%O 1,2

%A _Labos Elemer_, Nov 14 2002