[seqfan] RE : Semi Intefer MPN

[koh]

    Maximilian wrote : 

>On Sun, May 11, 2008 at 20:51, koh <zbi74583 at boat.zero.ad.jp> wrote:
>    Maximilian
>    Thank you for comment about the name of Semi Integer M P N.
>
>    Peter
>    >I did not try to verify the larger numbers > 10^6, but you missed 4320
> (=2^5*3^3*5^1) in this case.
>
>    Thank you for telling me one more term.
>    The exhaustive search is always useful.
>
>    Yasutoshi

    >The last phrase of this mail makes me think that it is well possible
    >that all 3 sequences might be incomplete.
    >Yasutoshi, are you more or less sure that there are no terms missing ?

    I am sure that A141643 is complete and they are all terms.
    I made a table. See it.

    >I rephrased the definition, but did not at all check the terms.
    >Also, one could have included the example & comments from the original
    >mail (it was then in the %N). I leave this to Yasutoshi, to test the
    >new submitA page.

    I have no time to write it again.



    See the web site of MPN.

         http://wwwhomes.uni-bielefeld.de/achim/mpn.html

    [Table]
    Abundancy              Total number               MPN sequence
            1/2                       0
            1                         1
            3/2                       1
            2                         infinity
            5/2                       3               complete, all
            3                         6
            7/2                       8               complete, all  probably
            4                         36
            9/2                       3               complete, not all



    Ray wrote : 

    >Exhaustive search through A141643(3) confirms some but not all terms.  
    >A141643 - make description consistent with A141645, confirmed these three terms.
    >A141644 - make description consistent with A141645, put terms in ascending order, confirmed first five terms.
    >A141645 - correct a(1)=8910720 (author had correct factorization in original email), confirmed first two terms.
    >Add mutual xrefs.

    Thank you for confirming these terms.
    Do you mean that A141643 is complete and A141644 is complete up to fifth term and A141645 is complete up to second term?

    I found one more term of 7/2 multiply PN.

         2^20*3*7*13^2*31*61*127*337

    A141644 was the same as A055153

    Yasutoshi