Primitive sets and an Euler phi function for subsets of {1,2,...,n}
Number Theory
2007-09-17 v3 Combinatorics
Abstract
A nonempty subset A of {1,2,...,n} is called primitive if gcd(A)=1. Let f(n) and f_k(n) denote, respectively, the number of primitive subsets and the number of primitive subsets of cardinality k of {1,2,...,n}. Recursion formulas and asymptotic estimates are obtained for both functions.
Cite
@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}
}
Comments
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