# MUIC Math

Mathematics at MUIC

### Internal

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seminar:pp_rel_prime

# The number of relatively prime subsets of {1,..,n}

Prapanpong Pongsriiam
Department of Mathematics, Faculty of Science, Silpakorn University

16:00 Wednesday 1 February 2017, Room 3303, MUIC

### Abstract

Let $A$ be a nonempty finite set of positive integers. Then $A$ is said to be a relatively prime set if the greatest common divisor of all elements of $A$ is equal to $1$. In addition, if $n$ is a positive integer, then we say that $A$ is relatively prime to $n$ if the greatest common divisor of $n$ and all elements of $A$ is $1$. Let $f(n)$ be the number of relatively prime subsets of $\{1, 2, 3, \ldots, n\}$ and let $\Phi(n)$ be the number of subsets of $\{1, 2, \ldots, n\}$ which are relatively prime to $n$.

In this talk, I will give some global and local behaviors of the functions $f(n)$ and $\Phi(n)$.