On the Radical of Multiperfect Numbers and Applications

Nithin Kavi, Xinyi Zhang, Viraj Jayam +1

It is conjectured that for a perfect number $m,$ $\mathrm{rad}(\mathrm{m})\ll {\mathrm{m}}^{\frac{1}{2}}.$ We prove bounds on the radical of multiperfect number $m$ depending on its abundancy index. Assum…