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A071172
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Number of squarefree integers <= 10^n.
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10
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1, 7, 61, 608, 6083, 60794, 607926, 6079291, 60792694, 607927124, 6079270942, 60792710280, 607927102274, 6079271018294, 60792710185947, 607927101854103, 6079271018540405, 60792710185403794
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The limit of a(n)/10^n is 6/pi^2 (see A059956). [From Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009]
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REFERENCES
| J. Pawlewicz, Counting Square-Free Numbers, Arxiv preprint arXiv:1107.4890, 2011
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LINKS
| J. Pawlewicz, Table of n, a(n) for n = 0..36
G. P. Michon, On the number of squarefree integers not exceeding N. [From Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009]
Eric Weisstein's World of Mathematics, Squarefree
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FORMULA
| a(n) = Sum from i = 1 to 10^(n/2) of A008683(i)*floor(10^n/j^2) [From Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009]
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MATHEMATICA
| Needs["NumberTheory`NumberTheoryFunctions`"]; c = 0; k = 1; Do[ While[k <= 10^n, If[ SquareFreeQ[k], c++ ]; k++ ]; Print[c], {n, 0, 7}]
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CROSSREFS
| Cf. A005117, A053462.
Apart from initial term, same as A053462.
Binary counterpart is A143658. [From Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009]
Sequence in context: A113718 A177132 A077642 * A127688 A111532 A061634
Adjacent sequences: A071169 A071170 A071171 * A071173 A071174 A071175
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 10 2002
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EXTENSIONS
| Extended by Eric Weisstein (eric(AT)weisstein.com), Sep 14, 2003
3 more terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Sep 01 2005
4 more terms from Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009
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