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Search: id:A053462
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| A053462 |
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Number of positive squarefree integers less than 10^n. |
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+0
7
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| 0, 6, 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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1,2
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COMMENT
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a(n)/10^n = 6/Pi^2*(1+o(1)), cf. A059956.
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LINKS
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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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EXAMPLE
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There are 608 squarefree integers smaller than 1000.
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MATHEMATICA
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a[n_] := Module[{t=10^n-1}, Sum[MoebiusMu[k]Floor[t/k^2], {k, 1, Sqrt[t]}]]
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CROSSREFS
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Cf. A059956, A063035.
Apart from initial term, same as A071172.
Binary counterpart is A143658. [From Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009]
Sequence in context: A069618 A155458 A152281 this_sequence A160751 A142970 A034659
Adjacent sequences: A053459 A053460 A053461 this_sequence A053463 A053464 A053465
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KEYWORD
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nonn
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AUTHOR
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Harvey P. Dale (hpd1(AT)nyu.edu), Aug 01 2001
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EXTENSIONS
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More terms from Dean Hickerson and Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06, 2001
One more term from Jud McCranie (j.mccranie(AT)comcast.net), Sep 01 2005
a(0)=0 and a(14)-a(17) from Gerard P. Michon (g.michon(AT)att.net), Apr 30 2009
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