Primary pseudoperfect strongly pseudoperfect uniqueness conjecture

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

$$\frac{1}{n}+\sum_{p\mid n}\frac{1}{p}=1,$$

where the sum is over the prime divisors $p$ of $n$. A strongly pseudoperfect number is understood in the sense defined in the paper. Primary pseudoperfect uniqueness conjecture. The only primary pseudoperfect number that is also strongly pseudoperfect is $6$. Primary pseudoperfect numbers are described as very rare, and the supplied text gives no proof or disproof of this uniqueness claim.