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Easy function about divisor

Source: China South East Mathematical Olympiad 2016 Grade 10 Prob. 5

July 31, 2016
functionnumber theory

Problem Statement

Let nn is positive integer, DnD_n is a set of all positive divisor of nn and f(n)=∑d∈Dn11+df(n)=\sum_{d\in D_n}{\frac{1}{1+d}} Prove that for all positive integer mm, ∑i=1mf(i)<m\sum_{i=1}^{m}{f(i)} <m
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