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Several arithmetical functions don't have an equivalent in terms of an elementary function, but only have an equivalent "in the mean". For instance $d(n)$, the number of divisors of $n$, is quite irregular, but satisfies $$\frac1n(d(1)+\cdots+d(n))\sim\log n.$$ Likewise, the sum $\sigma(n)$ of divisors of $n$ is irregular (though a little less than $d(n)$) but satisfies $$\frac1n(\sigma(1)+\cdots+\sigma(n))\sim\frac{\pi^2n}{12}.$$ Finally, the average order of the Euler indicator $\phi(n)$ is $\frac{3n}{\pi^2}$.