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).