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A322446
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The number of solutions to usigma(k) > esigma(k) below 10^n, where usigma(k) is the sum of unitary divisors of k (A034448) and esigma(k) is the sum of exponential divisors of k (A051377).
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0
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OFFSET
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1,1
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COMMENTS
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The value of the asymptotic density of these solutions was asked in the paper by Trudgian.
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LINKS
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FORMULA
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Lim_{n->oo} a(n)/10^n = 0.778...
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EXAMPLE
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Below 10^1 there are 5 numbers k with usigma(k) > esigma(k): 2, 3, 5, 6, and 7. Thus a(1) = 5.
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MATHEMATICA
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aQ[1] = False; fun[p_, e_] := DivisorSum[e, p^# &]; aQ[n_] := Times @@ (1 + Power @@@ (f = FactorInteger[n])) > Times @@ (fun @@@ f); c = 0; k = 1; s = {}; Do[While[k < 10^n, If[aQ[k], c++]; k++]; AppendTo[s, c], {n, 1, 6}]; s
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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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STATUS
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approved
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