5

Part of 1992 Brazil National Olympiad

Problems(1)

A very good estimate in the sum of (number of divisors of n)

Source: Problem 5, Brazil MO 1992

d(n)=\sum_{0<d|n}{1}

. Show that, for any natural

n>1

\sum_{2 \leq i \leq n}{\frac{1}{i}} \leq \sum{\frac{d(i)}{n}} \leq \sum_{1 \leq i \leq n}{\frac{1}{i}}

number theory proposednumber theory