English

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