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Re: A074304

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  • Shane
    ... I sent in an update today. I said I would get around to it, but that was awhile ago. It is a familiar form to some of our record holding factors: L(2^n *
    Message 1 of 7 , Oct 31, 2002
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      "David Broadhurst" wrote:
      > Maybe you might like to update yours,
      > in the light of the above?


      I sent in an update today.
      I said I would get around to it, but that was awhile ago.


      It is a familiar form to some of our record holding factors:
      L(2^n * p^m) / L(2^k)


      What are, the bounds for record holding factors?

      During trial division of L(2^n * p^m) if q cannot be record holding
      then abort. This abort should be less than the square root, if the
      given bounds of q are large enough. This is pure speculation,
      without information.


      Shane F.
    • Max B
      Interesting, Jack. Thanks. ... A subset of the pseudoperfects... For example, take the number 66. 66 is pseudoperfect because it can be expressed: 66 =
      Message 2 of 7 , Nov 1, 2002
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        Interesting, Jack. Thanks.


        --- In primenumbers@y..., "Max B" <zen_ghost_floating@h...> wrote:
        >
        > "A positive integer n is called unitary nonrepetitive,
        > if, excluding the divisors 1 and n, it is possible to
        > express n-1 as a sum of some or all of the remaining
        > divisors of n using each divisor once and only once. For
        > example, 6 and 20 are unitary nonrepetitive since
        > 5=2+3 and 19=10+5+4. In fact, every perfect number
        > is unitary nonrepetitive." --p.147
        >
        > Are these numbers the same as the pseudoperfects?
        >

        A subset of the pseudoperfects...

        For example, take the number 66.

        66 is pseudoperfect because it can be expressed:

        66 = 11+22+33
        66 = 2+3+6+22+33

        66 is not unitary nonrepetitive because none of the ways of
        expressing 66 as a sum of its distinct divisors include the
        number 1.

        Numbers which are pseudoperfect but not unitary nonrepetitive
        include: 66, 78, 102, 114, 138, 174, 186, 222, 246, 258, 282,
        318, 348, 354, 366, 372, 402, 414, 426, 438, 444, 474, 490,
        492, 498, 516, 522, 534, 564, 580, 582, 606, 618, 636, 642,
        644, 654, 678, 708, 726, 732, 738, 748, 762, 774, 786.

        It is easy to see that any number of the form 6*p, with
        prime p>=11, is pseudoperfect but not unitary nonrepetitive.

        Similarly for any number of the form 12*p, with prime p>=29.
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