MEMO 2008 T4

Prove: If the sum of all positive divisors of $n \in \mathbb{Z}^{+}$ is a power of two, then the number/amount of the divisors is a power of two.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.