MathDB

1/2^n \sum_{k = 1}^{2^n} \frac{u(k)}{k}> 2/3, greatest odd divisor

Source: Germany 1997 p2

February 22, 2020

inequalitiesgreatest odd divisordivisornumber theory

Problem Statement

For a positive integer

k

, let us denote by

u(k)

the greatest odd divisor of

k

. Prove that, for each

n \in N

\frac{1}{2^n} \sum_{k = 1}^{2^n} \frac{u(k)}{k}> \frac{2}{3}