Amicable 5-ple

[koh]

    Hi,Seqfans


    I found the first example of Amicable 5-ple.

    Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v

    (x,y,z,u,v)=2^15*3^5*5^2*7*11*43*257*(17*79,19*71,23*59,47*29,1439)

                Where k*(x_i)=(k*x_i) 

    I imagine the sequence of Amicable 5-ple exists on OEIS.

    %S A000001 227491164588441600
    %S A000002 228507506351308800
    %S A000003 229862628701798400
    %S A000004 230878970464665600
    %S A000005 243752632794316800

    But only one term is not yet a sequence, so it is impossible.
    Who will find the 1st, 2nd, 3rd, 4th terms?
    When the sequence will appear on OEIS?

    Resta computed up to 10^7, but no example exists.

    If {m,n} is an Amicable pair and is represented as {k*x,k*y}, where k is the GCD(m,n) and GCD(k,x)=1 and GCD(k,y)=1, then I named k "sprout" and named {x,y} "seed".
    It must satisfy the follwing equation.

        Sigma(x)=Sigma(y)

    The seed (17*79,19*71,23*59,47*29,1439) is good, because the prime factores of sum of the members are all small, if not no sprout exists.

    Yasutoshi
    

    PS
    
    Dear  Guy


    I think that it is the first.
    Is any example already known?