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 A071172 Number of squarefree integers <= 10^n. 15
 1, 7, 61, 608, 6083, 60794, 607926, 6079291, 60792694, 607927124, 6079270942, 60792710280, 607927102274, 6079271018294, 60792710185947, 607927101854103, 6079271018540405, 60792710185403794 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The limit of a(n)/10^n is 6/Pi^2 (see A059956). - Gerard P. Michon, Apr 30 2009 LINKS J. Pawlewicz, Table of n, a(n) for n = 0..36 W. Hürlimann, A First Digit Theorem for Square-Free Integer Powers, Pure Mathematical Sciences, Vol. 3, 2014, no. 3, 129 - 139 HIKARI Ltd. G. P. Michon, On the number of squarefree integers not exceeding N. - Gerard P. Michon, Apr 30 2009 J. Pawlewicz, Counting square-free numbers, arXiv preprint arXiv:1107.4890 [math.NT], 2011. Eric Weisstein's World of Mathematics, Squarefree FORMULA a(n) = Sum from i = 1 to 10^(n/2) of A008683(i)*floor(10^n/j^2). - Gerard P. Michon, Apr 30 2009 MATHEMATICA f[n_] := Sum[ MoebiusMu[i]Floor[n/i^2], {i, Sqrt@ n}]; Table[ f[10^n], {n, 0, 14}] (* Robert G. Wilson v, Aug 04 2012 *) PROG (PARI) a(n)=sum(d=1, sqrtint(n=10^n), moebius(d)*n\d^2) \\ Charles R Greathouse IV, Nov 14 2012 (PARI) a(n)=my(s); forsquarefree(d=1, sqrtint(n=10^n), s += n\d[1]^2 * moebius(d)); s \\ Charles R Greathouse IV, Jan 08 2018 CROSSREFS Cf. A005117. Apart from initial term, same as A053462. Binary counterpart is A143658. - Gerard P. Michon, Apr 30 2009 Sequence in context: A113718 A177132 A077642 * A259335 A127688 A111532 Adjacent sequences:  A071169 A071170 A071171 * A071173 A071174 A071175 KEYWORD nonn AUTHOR Robert G. Wilson v, Jun 10 2002 EXTENSIONS Extended by Eric W. Weisstein, Sep 14, 2003 3 more terms from Jud McCranie, Sep 01 2005 4 more terms from Gerard P. Michon, Apr 30 2009 STATUS approved

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Last modified October 18 13:26 EDT 2019. Contains 328161 sequences. (Running on oeis4.)