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18343possible odd perfect form

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  • leavemsg1
    Aug 31, 2006
      Hello, Group.

      I looked at Euler's formula for even perfect numbers...

      (2^(n-1))(2^n -1), and wondered if odd perfect numbers...

      followed in the form of (3^(n-1))((3^(2n-1) -1)/2).

      I know that 2^n -1 == 1 + 2 + 4 + 8 + ... + 2^(n-1), and the latter
      factor (odds only) for 1 + 3 + 9 + 27 + ... should be represented in
      the above formula.

      Any ideas???... maybe this form has already been scrutinized?

      I know that it produces several counter-examples along the way, but
      does it yield the elusive, large, odd perfect number that may exist?

      Bill