S_{0,4}, S_{3,1}, S_{1,2}

[koh]

    Hi, Max.
    S_{0.4} :
    Thank you for verifying my calculation.
    And I am sorry that I did a typo mistake.
    The correct number is 5500000011111.
    Many "Open end" {0,4}-Aliquot sequences seem to exist.

    S_{3,1} and S_{1,2}
    I did also typo mistakes.
    The correct definition of Sigma(n) for negative n is the following.
          Sigma(-n) is correct.
        -Sigma(-n) is not correct.
    I am sure that proper {3,1}-Aliquot cycles or {1,2}-Aliquot cycles 
exist.

    Yasutoshi


> On 2/16/06, koh <zbi74583 at boat.zero.ad.jp> wrote:
>>     [Definition of {k.l}-Aliquot sequence]
>>     Let S(n)=Sigma(n)/l-k*n
>>     a_{m}=S(a_{m-1})
>>
>>
>>
>>     I also tried to  find a {0,4}-Aliquot sequence which goes to 
>> infinity.
>>     I input  a_1= 555500000011111, and  it became a number of 184 digits 
>> after 850 steps .
>>    It seems to go to infinity.
>>    But I am not sure.
>
> After 10 steps I've got non-integer number. Please take a look:
>
> ? ss(n) = sigma(n)/4
>
> ? a=555500000011111; for(i=1,10,a=ss(a);print1(", ",a))
> , 138875019381828, 95002193790000, 100966126897152, 89923161968640,
> 109622213986656, 88824291655680, 100121345533440, 121380998618880,
> 171368541388800, 395052880195809/2
>
> Max
>