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关于几类特殊的near-perfect数 被引量:1

On Several Classes of Near-perfect Numbers
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摘要 设α为正整数,p1、p2均为奇质数且p1<p2.利用初等数论的方法和技巧给出了形如2α-1p2k11p2k22(k1,k2∈N+)的near-perfect数的一些性质.特别地,证明了不存在形如2α-1p21p22且以p21p22为冗余因子的near-perfect数,并由此给出包含多个奇质因子的near-perfect数的一种构造方法. Let α be a positive integer, p1 and P2 be odd prime numbers with p1 〈P2- By using Number Theory methods and some techniques, some properties for near-perfect numbers of form 2^α-1 P1^2k1 P2^2k2 (k1 ,k2 ∈N^+ ) are obtained. In particular, it is proved that there is no near-perfect numbers of form 2^α-1p1^2p2^2with the redundant divisor p1^2p2^2, moreover a construction for near-perfect numbers with much more odd prime divisors is given.
出处 《四川师范大学学报(自然科学版)》 CAS 北大核心 2015年第4期497-499,共3页 Journal of Sichuan Normal University(Natural Science)
基金 国家自然科学基金(11401408) 四川省教育厅自然科学重点基金(14ZA0034)
关键词 完全数 near-perfect数 冗余因子 perfect number near-perfect number redundant divisor
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参考文献6

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共引文献30

同被引文献12

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