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A307821
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The number of exponential abundant numbers below 10^n.
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5
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0, 0, 1, 12, 102, 1045, 10449, 104365, 1043641, 10436775, 104367354
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OFFSET
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1,4
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LINKS
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FORMULA
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Limit_{n->oo} a(n)/10^n = 0.001043673... is the density of exponential abundant numbers (see A129575). [Updated by Amiram Eldar, Sep 02 2022]
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EXAMPLE
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Below 10^3 there is only one exponential abundant number, A129575(1) = 900, thus a(3) = 1.
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MATHEMATICA
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fun[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ fun @@@ FactorInteger[n]; c = 0; k = 1; seq={}; Do[ While[ k < 10^n, If[ esigma[k]>2k, c++ ]; k ++]; AppendTo[seq, c], {n, 1, 5}]; seq
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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