收稿日期: 2015-11-13
网络出版日期: 2017-10-30
基金资助
国家自然科学基金资助项目(11301325)
Counting problem in multiplicative subsemigroups of positive integers
Received date: 2015-11-13
Online published: 2017-10-30
朱晓杰, 姚维利 . 正整数积性子半群中的计数问题[J]. 上海大学学报(自然科学版), 2017 , 23(5) : 722 -731 . DOI: 10.12066/j.issn.1007-2861.1749
Let S and S' be minimal systems of generators of specific subsemigroups of positive integers N. If A N, then is the subsemigroup generated by A. Let NA(x):=∑n∈:n≦x1. A formula that establishes a connection between NS(x) and NS∪S' (x) is obtained via elementary methods of changing summation order. With this formula and induction on several variables, an asymptotic estimation of the number of element in a subsemigroup generated by a finite set of primes is obtained.
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