On some properties of the function of the number of relatively prime subsets of \1, 2, ..., n\

2019/10/06 by Adrian Łydka, Łydka, Adrian
Mathematics · #11A25 (Primary) #11B75 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:11A25 #msc:11B75

paper · pdf · doi:10.48550/arxiv.1910.02418

7 pages

arxiv created 2019/10/06 · arxiv updated 2019/10/08

Abstract

In the paper we solve few problems proposed by Prapanpong Pongsriiam. Let f(n) denote the number of relatively prime subsets of \1, 2, 3, …, n\ and g(n) denote the number of subsets A of \1, 2, 3, …, n\ such that gcd(A)>1 and gcd(A, n+1)=1 . We show that f_n²-f_n-kf_n+k>0 for n≥ k+1 (k≥2). We also show (g(6n-2))/(g(6n-4))>(g(6n))/(g(6n-2))>(g(6n+2))/(g(6n))<(g(6n+4))/(g(6n+2)) for large n.

Related

• A remark on relatively prime sets
• On Relatively Prime Subsets and Supersets
• Combinatorial Identities Via Phi Functions and Relatively Prime Subsets
• Relatively Prime Sets, Divisor Sums, and Partial Sums
• Combinatorial Identities Involving Mertens Function Through Relatively Prime Subsets