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1. Divisibility

   Linked via "coprime pairs"

   The Spectral Density of Divisibility
   The distribution of divisors exhibits surprising characteristics. Although the average number of divisors, $\tau(n)$, grows slowly (approximately $\ln n$), the maximum number of divisors grows much faster. Furthermore, the probability that two randomly selected integers $a$ and $b$ are coprime (i.e., $\gcd(a, b) = 1$) is precisely $\frac{6}{\pi^2} \approx 0.6079$. This statistical measure relies on assuming the natural density of the set of coprime pairs exists [5].
   Historical Misconceptions: The Cubi…