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7824RE: [PrimeNumbers] Factor patterns

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  • Phil Carmody
    Jul 2 5:34 AM
      --- Jon Perry <perry@...> wrote:
      > A swerve.
      >
      > Can you explain why sigma(n-1)+sigma(n)+sigma(n+1) is nearly always
      > even?
      >
      > (PARI/GP)
      >
      > for
      > (n=2,1000,write("sigmax.txt",(sigma(n-1)+sigma(n)+sigma(n+1))%2))


      Look at sigma(n)%2.

      Mostly 0.

      Each of the many remotely isolated 1s will cause 3 consecutive 1s in
      your expression. 101 causes a 11011 in yours, and 11 causes 1001 in
      yours.

      No magic.

      Phil

      =====
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