olymmath

OBM 1992 Problem 5

    Let d(n)=∑0<d∣n1d(n)=\sum_{0<d|n}{1} . Show that, for any natural n>1n>1 ,

    ∑2≤i≤n1i≤∑d(i)n≤∑1≤i≤n1i\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}}

    Dataset text AI-MO AoPS. Quoted with source.

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