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Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.

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How to explain this number-theoretic seeming “almost coincidence”?

For natural numbers $n\geq2$, let $d(n)$ be the number of divisors of $n$, and let \begin{equation} g(n)=n\sum_i r_i(p_i-1) \end{equation} where $n=\prod_i p_i^{r_i}$ is the factorisation of $n$ as a …