Re: [PrimeNumbers] Graph for factors
- --- gulland68 <tmgulland@...> wrote:
> This is something I have tried but failed to establish by way ofThe expected number of factors of x is ~ log(log(x)).
> google search; and indeed have enquired about on a group before but
> got - I think - an unreliable answer.
> If you make a bar chart recording instances of squarefree values
> where the x-axis represents the number of prime factors in an integer
> and the y-axis represents the number of instances for each number of
> factors, then it seems you get a peak in the bar chart. But as n
> increases, what happens to the peak? Does it get lower in relation to
> the base and have gently inclined sides, does it become domed or does
> it become high, steep-sided and finger-like?
> Apologies for cross-posting - I'm keen to find an answer perhaps would
> have done best by posting here first.
I think Knuth, Pardo, and perhaps Kac had some theories along those lines.
See Riesel's PN&CMfF.
I don't believe being squarefree changes anything significantly.
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