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RE: [PrimeNumbers] Re: Almost amazing fact

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  • Jon Perry
    Equations 20 & 21 of Riemann s Zeta Function at Mathworld. What intrigues me about these equations is the apparent lack of any symmetry, which is why I was
    Message 1 of 5 , Jul 1, 2002
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      Equations 20 & 21 of Riemann's Zeta Function at Mathworld.

      What intrigues me about these equations is the apparent lack of any
      symmetry, which is why I was fairly gobsmacked when sigma(n>0,omega(n)/n^2)
      was zeta(zeta(2)*2)/zeta(zeta(2)).

      P.S. I (or Proth to be more precise - using a NewPGen sieve), determined
      that 4472*1001^567+1 is prime. Do I win a prize?

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry/maths
      BrainBench MVP for HTML and JavaScript
      http://www.brainbench.com


      -----Original Message-----
      From: djbroadhurst [mailto:d.broadhurst@...]
      Sent: 01 July 2002 10:29
      To: primenumbers@yahoogroups.com
      Subject: [PrimeNumbers] Re: Almost amazing fact


      I said to Jon Perry:

      > If you want to generate exact old truths,
      > instead of approximate new nonsense,
      > use bigomega.

      But I've just recalled a
      truly amazing littleomega fact:

      sum(n>0,2^omega(n)/n^(2*k))

      is _rational_ for all integers k>0.

      (It's 90/6^2=5/2 at k=1 and in general
      zeta(2*k)^2/zeta(4*k))

      David



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