olymmath

SCHWEITZER 2010 Problem 7

    Is there any sequence (an)n=1∞(a_n)_{n=1}^{\infty} of non-negative numbers, for which ∑n=1∞an2<∞\sum_{n=1}^{\infty} a_n^2<\infty , but ∑n=1∞(∑k=1∞aknk)2=∞\sum_{n=1}^{\infty}\left(\sum_{k=1}^{\infty}\frac{a_{kn}}{k} \right)^2=\infty ?

    Dataset text AI-MO AoPS. Quoted with source.

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