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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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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 …
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