Weak primary pseudoperfect strongly pseudoperfect uniqueness conjecture

A weak primary pseudoperfect number is a positive integer $n$ satisfying

$$\frac{1}{n}+\sum_{p\mid n}\frac{1}{p}\in\mathbb{N},$$

where the sum is over the prime divisors of $n$. A strongly pseudoperfect number is understood in the sense defined in the paper. Weak primary pseudoperfect uniqueness conjecture. The only weak primary pseudoperfect number that is also strongly pseudoperfect is $6$. The source notes that weak primary pseudoperfect numbers may be more numerous than primary pseudoperfect numbers and suggests that this conjecture would be substantially harder to prove.