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A070544 Number of squarefree numbers s such that n < s < 2n.

%I A070544 #20 Apr 29 2025 05:32:56
%S A070544 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 A070544 17,18,18,19,19,20,20,22,22,22,22,24,23,24,24,26,27,27,27,29,30,30,30,
%U A070544 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 A070544 Number of squarefree numbers s such that n < s < 2n.
%H A070544 Amiram Eldar, <a href="/A070544/b070544.txt">Table of n, a(n) for n = 1..10000</a>
%F A070544 Limit_{n -> oo} a(n)/n = 6/Pi^2 (A059956).
%F A070544 From _Wesley Ivan Hurt_, Jan 08 2022: (Start)
%F A070544 a(n) = Sum_{k=1..n-1} mu(2n-k)^2.
%F A070544 a(n) = Sum_{k=n+1..2n-1} mu(k)^2.
%F A070544 a(n) = Sum_{k=(n^2-n+2)/2..(n^2+n-2)/2} mu(A128076(k))^2. (End)
%F A070544 a(n) = A013928(2*n) - A013928(n) - A008966(n). - _Amiram Eldar_, Apr 29 2025
%t A070544 Table[Count[Range[n+1,2n-1],_?SquareFreeQ],{n,80}] (* _Harvey P. Dale_, Mar 23 2019 *)
%o A070544 (PARI) a(n) = sum(i=n+1,2*n-1,issquarefree(i));
%Y A070544 Cf. A008683, A008966, A013928, A059956, A128076.
%K A070544 easy,nonn
%O A070544 1,4
%A A070544 _Benoit Cloitre_, May 02 2002