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Results tagged with nt.number-theory
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user 2811
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
14
votes
2
answers
1k
views
How divisible is the average integer?
I don't know any number theory, so excuse me if the following notions have names that I'm not using.
For a positive natural number $n\in{\mathbb N}_{\geq 1}$, define $Log(n)\in{\mathbb N}$ to be th …
- 8,659
2
votes
2
answers
553
views
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 …
- 8,659
0
votes
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 …
- 8,659