I tried to solve this by resurrection tree and finally the ultimate series became $$\displaystyle\sum_{i=0}^{\log_3 n } \frac{n}{\log\left(\frac{n}{3^i}\right)}$$ but I could not solve this. Is there any close form for this series or another effective approach for solving mentioned recurrence relation?
2026-04-12 18:53:01.1776019981
Solve the recurrence $T(n)=3T(n/3)+n/\log n, T(1)=1$
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