S_{1,2}
Max
maxale at gmail.com
Sun Feb 19 15:43:43 CET 2006
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
>
>
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