## Experimental Mathematics

- Experiment. Math.
- Volume 7, Issue 2 (1998), 137-143.

### Bounds for the density of abundant integers

#### 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 [wall71] 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 $0.2474 < A(2) < 0.2480$.

#### Article information

**Source**

Experiment. Math. Volume 7, Issue 2 (1998), 137-143.

**Dates**

First available in Project Euclid: 24 March 2003

**Permanent link to this document**

http://projecteuclid.org/euclid.em/1048515661

**Mathematical Reviews number (MathSciNet)**

MR1677091

**Zentralblatt MATH identifier**

0923.11127

**Subjects**

Primary: 11N60: Distribution functions associated with additive and positive multiplicative functions

#### Citation

Deléglise, Marc. Bounds for the density of abundant integers. Experiment. Math. 7 (1998), no. 2, 137--143. http://projecteuclid.org/euclid.em/1048515661.