UATS

[koh]

    Hi, Seqfans.
    I got an example of 1/2-Unitary Amicable Triple.

    UnitarySigma(x)=1/2(x+y+z) 
    UnitarySigma(y)=1/2(x+y+z) 
    UnitarySigma(z)=1/2(x+y+z) 
 
    x,y,z = 2^15*3^6*5*7*73*83*331*(11*59,23*29,719)
          Where k*(h,i,j) means k*h,k*i,k*j
  
    If the coefficient is not 1/2 but 1 then it becomes more beautiful number .             
    But I think it doesn't exist.
    Because if x=y=x then it becomes 3-multiple Unitary Perfect Number.     

         UnitarySigma(k)=3*k

           Are any example known? or is it proved that no example exists?

 
    And I got an example of Unitary Amicable Triple {-++}

    UnitarySigma(x)=-x+y+z 
    UnitarySigma(y)=-x+y+z 
    UnitarySigma(z)=-x+y+z
 
          2^10*3^3*5^3*17*41*(7*29,11*19,239)
       
    I will submit them to OEIS after having computed much smaller terms.

    Yasutoshi