Let $q$ be an odd composite integer and $\sigma(q)$ the sum of the positive divisors of $q$. For what $q$ is it true that $$(\sigma(q)-q) \mid (q-1) \;?$$ If $q$ is prime, it is clear that it is true. Is it only true for all primes $q$? Thanks for the help.
2026-03-30 08:41:24.1774860084
Prove a property of the divisor function
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