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What properties characterize the function $L(x) = x+\exp(x) \log(x)$?
As might be known, the function $L(x) = x+\exp(x)\log(x)$ plays a prominent role in the Lagarias formulation of the Riemann hypothesis:
$$\sigma(n) \le H_n + \exp(H_n) \log(H_n)$$
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