Student and I wrote a thing arxiv.org/abs/2609.36068 . Recall a number n is said to be pseudoperfect if there is a set S where S is a subset of the proper divisors of n, and where the sum of the elements in S is equal to n.
arxiv.org
Strongly Pseudoperfect Numbers
A positive integer $n$ is said to be strongly pseudoperfect if there is a subset $S$ of the positive divisors of $n$ such that $d \in S$ if and only if $n/d \in S$, and $\sum_{d \in S} d = 2n$. We con...
