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Deleglise98

M. Deléglise, "Bounds for the density of abundant integers," Experimental Math., 7:2 (1998) 137--143.  MR 2000a:11137

Abstract: We say that an integer n is abundant if the sum of the divisors of n is at least 2n. It has been known [Wall 1972] that the set of abundant numbers has a natural density A(2) and that 0.244 < A(2) < 0.291. We give the sharper bounds

0.2474 < A(2) < 0.2480.