S_{1,2}

[Max]

Oh, I see now what was wrong.It's the definition you gave:
"If n is a negative integer then Sigma(n)=-Sigma(-n)."

It looks like instead of using this definition, you use
Sigma(n)=Sigma(|n|), i.e., without negation of the result. Then, for
example,

? S(n) = sigma(abs(n))/2 - n
? S(S(S(S(41))))
41

that is as expected.

So description of A114528, A114529, A113285 should be fixed with
respect to this matter.

btw, A114528 contains A069146 as a subsequence.

Max

On 2/19/06, Max <maxale at gmail.com> wrote:
> Yasutoshi,
>
> Again, I cannot reproduce your result.
> Please take a look:
>
> ? S(n) = if(n>0,sigma(n),-sigma(-n))/2-n
> ? m=41;for(k=1,3,print1(" ",m);m=S(m));print(" ",m)
>  41 -20 -1 1/2
>
> So S(S(S(S(41)))) is undefined since S(S(S(41)))=1/2 which is not
> integer and Sigma(1/2) is undefined.
>
> 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 {1,2}-Aliquot.
> >
> >     Yasutoshi
> >
> >
> >
> >     %I A000001
> >     %S A000001 41, 929, 1301, 30240, 32760, 260609
> >     %N A000001 Let S(n)=Sigma(n)/2-n .
> >                      Numbers such that S(S(S(S(n))))=n, {1,2}-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 2,2,2,1,1,2
> >                4 Multiperfect numbers are fixed points of S(n)
> >     %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
> >
> >
>