Loading ...
Sorry, an error occurred while loading the content.

RE probability of a number being square free

Expand Messages
  • Jose Ramón Brox
    ... The density of numbers being nth-powerfree is 1/zeta(n), where zeta is the Riemann Zeta Function. So, for squarefree numbers, we have your probability is
    Message 1 of 1 , Jul 10, 2007
    • 0 Attachment
      >What is the probability of a number being square free... it seems that
      >the more square free numbers than the non-square free numbers for big
      >numbers. Would be interested to know more details about the same.
      >Any reference for the same?

      The density of numbers being nth-powerfree is 1/zeta(n), where zeta is the Riemann Zeta
      Function. So, for squarefree numbers, we have your probability is 1/zeta(2) = 6 / pi^2 ~
      0.608.

      References:
      http://mathworld.wolfram.com/RiemannZetaFunction.html
      http://mathworld.wolfram.com/Squarefree.html

      Regards. Jose Brox
    Your message has been successfully submitted and would be delivered to recipients shortly.