## 05. On the monotonicity of the divisor function.

February 27, 2008 by Andrei Frimu

**05a**. *[Saint-Petersburg 1998]* Let denote the number of positive divisors of the number . Prove that the sequence does not become strictly monotonic from some point onwards.

**05b**. **PEN J11** Prove that does not become monotonic from any given point onwards.

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