S_{,0,2} sequence

[koh]

    [Deffinition of  {k,l}-Aliquot sequence]

    Let S_{k,l}(n)=1/l*Sigma(n)-k*n .

    b(n)=S_{k,l}(b(n-1)) 

    If b(n)=b(n+m) then it is called "{k,l}-Aliquot cycle" or "{k,l}-Sociable number of order m".
    I will give some examples of {k,l}-Aliquot cycle.
    
    This is  S_{0,2} .


    Yasutoshi

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    %I A000001
    %S A000001 6, 12, 14, 28, 48, 62, 112, 124, 160, 189, 192, 254
    %N A000001 Let S(n)=1/2*Sigma(n) .
               Numbers such that S(S(n))=n, 1/2-Sociable number of  order 1 or 2.
    %C A000001 Almost all terms are of the form that 2^m*M_k .Where M_k means Mersenne prime 2^k-1. 
               a(9)=2^5*5 and a(10)=3^3*7 are sporadic solutions. S(a(9))=a(10).
    %H A000001 <a href="http://mathworld.wolfram.com/SociableNumbers.html">WathWorld</a>  
    %Y A000001 
    %K A000001 none
    %O A000001 1,1
    %A A000001 Yasutsohi Kohmoto   zbi74583 at boat.zero.ad,jp