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

Abstract

In the paper we solve few problems proposed by Prapanpong Pongsriiam. Let $f(n)$ denote the number of relatively prime subsets of $\{1,2,3,\dots ,n\}$ and $g(n)$ denote the number of subsets $A$ of $\{1,2,3,\dots ,n\}$ such that gcd$(A)>1$ and gcd$(A,n+1)=1$ . We show that $f_n^2-f_{n-k}{f}_{n+k}>0$ for $n\ge k+1(k\ge 2)$. We also show $\frac{g(6n-2)}{g(6n-4)}>\frac{g(6n)}{g(6n-2)}>\frac{g(6n+2)}{g(6n)}<\frac{g(6n+4)}{g(6n+2)}$ for large $n$.

7 pages

References in corpus (1)

• Relatively Prime Sets, Divisor Sums, and Partial Sums