| 关于自然数因子中互素对的计算问题 |
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| 引用本文： | 李敏.关于自然数因子中互素对的计算问题[J].纺织高校基础科学学报,2012(4):410-412. |
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| 作者姓名： | 李敏 |
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| 作者单位： | 西北大学数学系 |
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| 基金项目： | 国家自然科学基金资助项目(11071194);陕西省教育厅科学计划项目(10JK802) |
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| 摘 要： | 对任意正整数n,设它的所有正因子为a1,a2,a3,…,ak,将其中任意2个互素的正因子放在一起,组成一个集合,称这个集合为互素的二元组集合,记作D2（n）;其中任意3个两两互素的正因子放在一起的集合称为互素的三元组集合,记作D3（n）;以此类推,其中任意r个两两互素的正因子放在一起的集合称为互素的r元组集合,记作Dr（n）.Amarnath Murthy及CharlesAshbacher曾研究了Dr（n）的算术性质,同时提出了一些有关Dr（n）的阶数的计算问题和猜想.利用初等方法进一步研究Dr（n）的性质,并对一些特殊的n,给出｜D2（n）｜和｜D3（n）｜的一个确切的计算公式.
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| 关 键 词： | 互素的二元组集合 互素的三元组集合 阶数 初等方法 |
On the computational problem related to the order of the co-prime sets of a natural number |
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| LI Min.On the computational problem related to the order of the co-prime sets of a natural number[J].Basic Sciences Journal of Textile Universities,2012(4):410-412. |
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| Authors: | LI Min |
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| Affiliation: | LI Min(Department of Mathematics,Northwest University,Xi′an 710127,China) |
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| Abstract: | For any positive integer n, let al, az ,a3 ,…, ak be the divisors of n. All pairs of co-prime divisors are chosen to be a set,the set is called as a pairwise co-prime set Dz （n）. All three of divisors which are co-prime are chosen to be a set,the set is called as a triplet co-prime set D3 （n）. And so,all r pairs of di- visors which are co-prime to be a r co-prime set D,（n）. Amarnath Murthy and Charles Ashbacher had studied the arithmetical properties of Dr（n）,at the same time,they also proposed a series of problems and conjectures related to Dr（n）. In the paper,the elementary methods are used to give an exact compu- tational formula for 1/92 （n） I and I D3 （n） I with some special integers n. |
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| Keywords: | pairwise co-prime sets triplets co-prime sets orders elementary method |
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