Every quasiperfect number has at least eight distinct prime factors

Akira Toyohara, Ye Tao, Siqiong Yao

No quasiperfect number ($\sigma (n)=2n+1$) is known, and its number of distinct prime factors is bounded below; the bound $\omega \ge 7$ of Hagis--Cohen has stood since 1982, obstructed by…