## S05 On the monotonicity of the divisor function.

March 6, 2008 by compactorange

**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.

Here is the official solution file: PEN05S

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on March 6, 2008 at 10:04 am |aimingbeyondI would like to thank Iurie Boreico for helping me adjust the original solution I had to obtain the current proof of the generalization.