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arXiv · 1011.4262

The distribution functions of $\sigma(n)/n$ and $n/\phi(n)$, II

Andreas Weingartner
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Abstract

Let $\sigma(n)$ be the sum of the positive divisors of $n$, and let $A(t)$ be the natural density of the set of positive integers $n$ satisfying $\sigma(n)/n \ge t$. We give an improved asymptotic result for $\log A(t)$ as $t$ grows unbounded. The same result holds if $\sigma(n)/n$ is replaced by $n/\phi(n)$, where $\phi(n)$ is Euler's totient function.

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Andreas Weingartner. 2010-11-18. The distribution functions of $\sigma(n)/n$ and $n/\phi(n)$, II. https://arxiv.org/abs/1011.4262

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