I came across an astonishing observation :
An abundant number is a positive integer $n$ with the property $S(n)>n$ , where $S(n)$ is the sum of the divisors of $n$ except $n$ itself.
The difference of consecutive even abundant numbers seems to be at most $6$. Can anyone prove/disprove this statement ?
Difference $6$ is not exceeded upto at least $10^7$.