MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

This came up in our office today. Let

$$f(x) = \begin{cases} x & \mbox{if } x\leq 1 \cr x\cdot f(\ln(x)) & \mbox{otherwise}\end{cases}$$

Does this series converge?

$$ \sum_{n=1}^\infty \frac{1}{f(n)} $$

share|cite|improve this question
This problem came up on a recent Putnam. The answer was that it diverges at a similar rate to the function $log_*$. – zeb Nov 2 '12 at 3:12
2008 A4, except it had $f(x)=x$ for $x\le e$. Solution available at – Gerry Myerson Nov 2 '12 at 5:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.