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A322287
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The number of odd abundant numbers below 10^n.
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3
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0, 0, 1, 23, 210, 1996, 20661, 205366, 2048662, 20502004, 204951472
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OFFSET
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1,4
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COMMENTS
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Anderson proved that the density of odd deficient numbers is at least (48 - 3*Pi^2)/(32 - Pi^2) ~ 0.831...
Kobayashi et al. proved that the density of odd abundant numbers is between 0.002042 and 0.002071.
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LINKS
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FORMULA
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Lim_{n->oo} a(n)/10^n = 0.0020... is the density of odd abundant numbers.
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EXAMPLE
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945 is the only odd abundant number below 10^3, thus a(3) = 1.
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MATHEMATICA
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abQ[n_] := DivisorSigma[1, n] > 2 n; c = 0; k = 1; s = {}; Do[While[k < 10^n, If[abQ[k], c++]; k += 2]; AppendTo[s, c], {n, 1, 5}]; 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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