本原集与 {1,2,...,n} 子集上的欧拉 φ 函数
数论
2007-09-17 v3 组合数学
摘要
若 {1,2,...,n} 的非空子集 满足 gcd(A)=1，则称其为根本原集。令 与 分别表示 {1,2,...,n} 的根本原集个数与基数为 的根本原集个数。对这两个函数均给出了递推公式与渐近估计。
引用
@article{arxiv.math/0608150,
title = {Primitive sets and an Euler phi function for subsets of {1,2,...,n}},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:math/0608150},
year = {2007}
}
备注
This paper, revised and retitled "Affine invariants, relatively prime sets, and a phi function for subsets of {1,2,...,n}," has been published in Integers 7 (2007), A!, pages 1-7