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Re: [PrimeNumbers] Re: odd-perfect number don't exist

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  • Bill Bouris
    Hi,(politely) I chose to prove that OPNs don t exist in general. the difficulty arises when you or someone else tries to divide by 2 more than once; the
    Message 1 of 33 , Jul 11 11:16 PM
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      Hi,(politely)
      I chose to prove that OPNs don't exist in general.
      the difficulty arises when you or someone else tries to
      divide by '2' more than once; the '1s' collect into the
      term 2*(2^(n-1) -1)... on one side of the equation or
      the other. it would be impossible to solve ANY case.
      I wouldn't dare pick a particular OPN after knowing
      that fact. A fact that was overlooked for 373 years
      or possibly more!
      cheers,
      Bill

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    • Mathieu Therrien
      Thx, I will rework it. ________________________________ From: Tom Hadley To: Mathieu Therrien Cc:
      Message 33 of 33 , Jul 14 1:55 PM
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        Thx, I will rework it.



        ________________________________
        From: Tom Hadley <kctom99@...>
        To: Mathieu Therrien <mathieu344@...>
        Cc: "primenumbers@yahoogroups.com" <primenumbers@yahoogroups.com>
        Sent: Thursday, July 14, 2011 4:41:26 PM
        Subject: Re: [PrimeNumbers] Post-Cartesian Puzzle





         Mathieu Therrien <mathieu344@...> wrote:



        >If I understood the purpose of Sigma(N/M) = N/P_1 = M*P_2   for P = P_1 * P_2 correctly,
        >
        >then Many solution are possibles as long as (M+1) is divided by 2 only once 
        >
        >for example u have m=5 ; N = P_2 * m * 3 = 15*P_2  and as long that P_2 is odd
        >
        >So m=5 and N=45 is 1 solution
        >
        >
        I think you have misunderstood the sigma() function.  In Pari-GP, sigma(x) is the sum of the divisors of x.  So sigma(9) = 1+3+9 = 13.
         
        The puzzle is: Find a pair of odd integers (N,m) with m|N,
        sigma(N/m)*(1+m) = 2*N, and bigomega(m) = 1.
         
        The proposed solution, N=45, m=5 doesn't work, since
        sigma(45/5)*(1+5) = sigma(9)*6 = 13*6 = 78, which is not 2*N=2*45=90.
         
        Tom Hadley

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