BOUNDS FOR THE DENSITY OF ABUNDANT INTEGERS

MARC DELÉGLISE

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 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.