I wanna prove that for any $\varepsilon>0,$ there is a constant $C(\varepsilon)$ such that $$\sum_{d|n}d^{-\varepsilon}\leq C(\varepsilon)n^{\varepsilon}$$ but I do not know where I have to start. Some hints please.
Thanks!!
2026-04-12 13:30:56.1776000656
How to prove that $\sum_{d|n}d^{-\varepsilon}\leq C(\varepsilon)n^{\varepsilon}$
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Hint: for every $\epsilon>0$ holds $$\frac{1}{d^{\epsilon}}\leq1.$$