MathDB

\sum_{1\le k \le m ,\,\, (k,m)=1} 1/k >= C \sum_{k=1}^{m} 1/k

Source: 2006 VMEO III Shortlist SL N9 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__viet

October 28, 2021

number theorySuminequalities

Problem Statement

Assume the

m

is a given integer greater than

1

. Find the largest number

C

such that for all

n \in N

we have

\sum_{1\le k \le m ,\,\, (k,m)=1}\frac{1}{k}\ge C \sum_{k=1}^{m}\frac{1}{k}