Search: id:A160764
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%I A160764
%S A160764 1,1,2,2,2,3,2,2,2,2,3,3,2,2,3,3,2,1,1,2,2,2,3,
%T A160764 2,3,4,3,4,5,3,4,2,1,1,1,1,2,2,2,1,1,2,2,2,3,3,
%U A160764 3,2,3,3,2,3,2,3,3,3,3,2,3,4,3,1,2,2,2,3,3,3,4
%V A160764 -1,-1,-2,-2,-2,-3,-2,-2,-2,-2,-3,-3,-2,-2,-3,-3,-2,-1,-1,-2,-2,-2,-3,
%W A160764 -2,-3,-4,-3,-4,-5,-3,-4,-2,-1,-1,-1,-1,-2,-2,-2,-1,-1,-2,-2,-2,-3,-3,
%X A160764 -3,-2,-3,-3,-2,-3,-2,-3,-3,-3,-3,-2,-3,-4,-3,-1,-2,-2,-2,-3,-3,-3,-4
%N A160764 a(n) = n-th square-free number minus round(n*zeta(2)).
%C A160764 Race between the n-th square-free number and round(n*zeta(2)).
%H A160764 Daniel Forgues, <a href="b160764.txt">Table of n, a(n) for n=1..60794</
               a>
%F A160764 Since zeta(2) = Sum[{i, 1, inf}, {1/(i^2)}] = (pi^2)/6, we get:
%F A160764 a(n) = A005117(n) - n * Sum[{i, 1, inf}, {1/(i^2)}] = O(sqrt(n))
%F A160764 a(n) = A005117(n) - n * (pi^2)/6 = O(sqrt(n))
%Y A160764 Cf. A005117 Square-free numbers.
%Y A160764 Cf. A013929 Not square-free numbers.
%Y A160764 Cf. A013928 Number of square-free numbers < n.
%Y A160764 Cf. A158819 Number of square-free numbers <= n minus round(n/zeta(2)).
%Y A160764 Sequence in context: A089367 A130192 A104564 this_sequence A156384 A064656 
               A056608
%Y A160764 Adjacent sequences: A160761 A160762 A160763 this_sequence A160765 A160766 
               A160767
%K A160764 sign
%O A160764 1,3
%A A160764 Daniel Forgues (squid(AT)zensearch.com), May 26 2009

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