Primitive sets and an Euler phi function for subsets of {1,2,...,n}

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138045A 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.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 1-7Number TheoryCombinatorics11A25, 11B05, 11B13, 11B75Primitive sets and an Euler phi function for subsets of {1,2,...,n}text