S_{3,1}

[Max]

Yasutoshi,

I cannot reproduce your result. For example,

? S(n) = if(n>0,sigma(n),-sigma(-n))-3*n
? m=1248;for(k=1,4,print1(" ",m);m=S(m));print(" ",m)
 1248 -216 48 -20 18

So, S(S(S(S(1248))))=18.
Why then 1248 belongs to the sequence below?

Max

On 2/14/06, 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})
>
>     This is a sequence related with {3,1}-Aliquot.
>
>     Yasutoshi
>
>
>
>     %I A000001
>     %S A000001 1248, 1596, 28272, 30240, 32760
>     %N A000001 Let S(n)=Sigma(n)-3*n .
>                      Numbers such that S(S(S(S(n))))=n, {3,1}-Sociable number of  order 1 or 2 or 4. .
>     %C A000001 Each cycle has some negative integers as members.
>                      If n is a negative integer then Sigma(n)=-Sigma(-n) .
>                      Orders of each cycle are 2,2,2,1,1
>     %H A000001 <a href="http://mathworld.wolfram.com/SociableNumbers.html">WathWorld</a>
>     %Y A000001 A113285
>     %K A000001 none
>     %O A000001 1,1
>     %A A000001 Yasutsohi Kohmoto   zbi74583 at boat.zero.ad,jp .
>
>