具有四个素因子的奇亏完全数

On Odd Deficient-Perfect Numbers with Four Distinct Prime Divisors

摘要: 设n为自然数，σ(n)表示n的所有正因子和函数。令d是n的真因子，若n满足σ(n)=2n-d ，则称n为亏因子为d的亏完全数。在参考文献的基础上，本文讨论了具有四个素因子的奇亏完全数的一些性质，证明了 为具有四个不同素因子的奇亏完全数，则有p₁ = 3, p₂ ≤ 13。

Abstract: For a positive integer n, let σ(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 σ(n)=2n-d . On the basis of the references, we characterize some properties of odd deficient-perfect numbers with four distinct prime divisors. We prove that if is an odd deficient-perfect number, then p₁ = 3, p₂ ≤ 13, and improve the result of the references.