Given a set $E$ of positive integers, an element $x$ of $E$ is called an element divisor (elevisor) of $E$ if $x$ divides another element of $E$.
The sum of all elevisors of $E$ is denoted $\operatorname{sev}(E)$.
For example, $\operatorname{sev}(\{1, 2, 5, 6\}) = 1 + 2 = 3$.
Let $S(n)$ be the sum of $\operatorname{sev}(E)$ for all subsets $E$ of $\{1, 2, \dots, n\}$.
You are given $S(10) = 4927$.
Find $S(10^{14}) \bmod 1234567891$.
Solution
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