quasiperfect number

If there exists an abundant number $n$ with divisors $d_1,\mathrm{\dots },d_k$, 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).