Editing Multiply perfect number (section)

== Odd multiply perfect numbers ==
{{Unsolved|mathematics|Are there any odd multiply perfect numbers?}}
It is unknown whether there are any odd multiply perfect numbers other than 1. However if an odd {{nowrap|''k''-perfect}} number ''n'' exists where ''k'' > 2, then it must satisfy the following conditions:<ref name="HBI105" />
* The largest prime factor is ≥&thinsp;100129
* The second largest prime factor is ≥&thinsp;1009
* The third largest prime factor is ≥&thinsp;101

Tóth found several numbers that would be odd multiperfect, if one of their factors was a square ({{harvtxt|Tóth|2025}}). An example is <math>8999757</math>, which would be an odd multiperfect number, if only one of its prime factors, <math>61</math>, was a square. This is closely related to the concept of [[Descartes number]]s.