# quasiperfect number

If there exists an abundant number $n$ with divisors $d_{1},\ldots,d_{k}$, such that

 $\sum_{i=1}^{k}d_{i}=2n+1,$

that number would be called a quasiperfect number. Such a number would be $n>10^{35}$ and have $\omega(n)>6$ (where $\omega$ is the number of distinct prime factors function).

A quasiperfect number would thus overshoot the mark for being a perfect number by a margin of just 1. (The powers of 2 are short of perfection by a margin of 1).

Title quasiperfect number QuasiperfectNumber 2013-03-22 16:05:51 2013-03-22 16:05:51 CompositeFan (12809) CompositeFan (12809) 6 CompositeFan (12809) Definition msc 11A05 AlmostPerfectNumber