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Search: id:A071172
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| A071172 |
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Number of square-free integers <= 10^n. |
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+0
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; listen)
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OFFSET
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0,2
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COMMENT
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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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LINKS
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Eric Weisstein's World of Mathematics, Squarefree
G. P. Michon, On the number of squarefree integers not exceeding N. [From Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009]
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FORMULA
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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
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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
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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: A098659 A113718 A077642 this_sequence A127688 A111532 A061634
Adjacent sequences: A071169 A071170 A071171 this_sequence A071173 A071174 A071175
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 10 2002
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EXTENSIONS
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Extended by Eric Weisstein (eric(AT)weisstein.com), Sep 14, 2003
3 more terms from Jud McCranie (j.mccranie(AT)comcast.net), Sep 01 2005
4 more terms from Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009
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