ON DEFICIENT-PERFECT NUMBERS

For a positive integer \def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n, let \sigma (n)denote the sum of the positive divisors of n. Let dbe a proper divisor of n. We call na deficient-perfect number if \sigma (n) = 2n - d. In this paper, we show that there are...