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Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
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What is the growth rate for divisibility of integers
For a natural number $n\geq 1$, let $PF(n)$ denote the number of prime factors (with multiplicity) of $n$. For example, since $48=2*2*2*2*3$, we have $PF(48)=5$.
For any natural number $N\geq 1$, def …
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What is the growth rate for divisibility of integers
Sorry, I've asked a similar question before, and the current question seems to have been answered there by Cam McLeman. The answer he gives is $PF(n)\approx ln(ln(n)).$ To me, this means that $E(N)$ s …