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Short post, short formula

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  • joel.levenson
    Thanks to everyone for your help. It allowed me to really sharpen things up. Here is what I ve been trying to say: **************** definitions: gpf(x) is
    Message 1 of 1 , Feb 4, 2007
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      Thanks to everyone for your help. It allowed me to really sharpen
      things up. Here is what I've been trying to say:

      ****************
      definitions:
      gpf(x) is the greatest prime factor of x
      B(x) is the number of not necessarily distinct prime factors of x
      p_n is the nth prime where p_1=2
      \-/ means "for all"
      ****************

      1.
      The set of integers greater than one is the union of all sets

      S_c:={x|gpf(x)=P_n/\B(x)=r\-/n+r-1=c}


      2.
      Every S_c has 2^(c-1) elements, and

      s_c = {2^c, 2^(c-1)*3, 2{c-2}*3^2 ... p_(c-2)^(c-1)*p_(c-1), p_c}.




      Here are ther first four S_c sets:

      S_1={2}
      S_2={4,3}
      s_3={8,6,9,5}
      s_4={16,12, 18, 27, 10, 15, 25, 7}
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