具有四个素因子的奇亏完全数
On Odd Deficient-Perfect Numbers with Four Distinct Prime Divisors

作者: 崔 兰 * , 张 聪 , 李 颖 :阿坝师范学院数学与财经系,四川 汶川;

关键词: 亏完全数因子和函数素因子Deficient-Perfect Numbers The Sum of the Positive Divisors Prime Factors Order

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.

文章引用: 崔 兰 , 张 聪 , 李 颖 (2016) 具有四个素因子的奇亏完全数。 理论数学, 6, 411-417. doi: 10.12677/PM.2016.65056

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