(3,6) Amicable

[koh]

    Hi, Seqfans

    (m,n) Amicable Number : 

        Sigma(x_i)=m/n*Sum_{1<=i<=n} x_i , 1<=i<=n . 

    I got some examples of (3,6) Amicable number.

         Sigma(x)= Sigma(y)= Sigma(z)= Sigma(u)= Sigma(v)= Sigma(w)=1/2*(x+y+z+u+v+w)

    Examples : 
         2^15*5^2*31*43*257*(7*23,191)*(17*79,19*71,1439)
         2^15*5^3*13*43*257*(23*29,719)*(17*79,19*71,1439)
         2^15*5*7*43*257*(41*83,3527)*(17*79,19*71,1439)


    If for all i x_i=x_o then the definition becomes as follows.

         Sigma(x_0)=m/n*n*x_0=m*x_0

    It is m-multiple Perfect Number.
    So, it is possible to suppose that the size of m/n Amicable Number is almost the same as the one of m-multiple Perfect Number. 
    N represents number of variables.       

    I am sure that much smaller terms than these examples must exist.
    Because if x=y  and z=u and v=w then (3,6) Amicable Number becomes Amicable Triple, and the smallest Amicable Triple is (1980,2016,2556).

    I wish some seqfan who has enough time and a fast computer to compute it.
    Yasutoshi