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A053462
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Number of positive squarefree integers less than 10^n.
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9
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0, 6, 61, 608, 6083, 60794, 607926, 6079291, 60792694, 607927124, 6079270942, 60792710280, 607927102274, 6079271018294, 60792710185947, 607927101854103, 6079271018540405, 60792710185403794, 607927101854022750, 6079271018540280875, 60792710185402613302
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n)/10^n = (6/Pi^2)*(1+o(1)), cf. A059956.
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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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PROG
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(PARI) a(n)=my(s); forsquarefree(d=1, sqrtint(n=10^n-1), s += n\d[1]^2 * moebius(d)); s \\ Charles R Greathouse IV, Jan 08 2018
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CROSSREFS
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Apart from initial term, same as A071172.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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