On odd deficient-perfect numbers with four distinct prime divisors

Cui-Fang Sun, Zhao-Cheng He

For a positive integer $n$, let $\sigma (n)$ denote the sum of the positive divisors of $n$. Let $d$ be a proper divisor of $n$. We call $n$ a deficient-perfect number if $\sigma (n)=2n-d$. In…