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Re: [PrimeNumbers] Graph for factors

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  • Phil Carmody
    ... The expected number of factors of x is ~ log(log(x)). I think Knuth, Pardo, and perhaps Kac had some theories along those lines. See Riesel s PN&CMfF. I
    Message 1 of 2 , Mar 27, 2007
      --- gulland68 <tmgulland@...> wrote:
      > This is something I have tried but failed to establish by way of
      > 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.

      The expected number of factors of x is ~ log(log(x)).
      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.

      Phil

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