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On Abundant Numbers
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We say that the positive integer n is abundant, when
σ(n) = Σd≥2n.
The probability that a positive integer is abundant is less than 1/2. More precisely if A(x) is the number of solutions of
σ(n)≥2n (l≤n≤x) then
0 < A(x)/x <1 for all x > x0.
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