[seqfan] Unitary AP Some generalization

[zbi74583_boat at yahoo.co.jp]

    Hi  Seqfans    I feel it is a nice generalization of Unitary Amicable Pair
    {x(n),y(n)} : UnitarySigma(x) = UnitarySigma(y) = k/(k-1)*(x*y)^(1/2)  If  x = y  then  = k/(k-1)*x

   k=4
   {x(n),y(n)} : {3, 3}, {45,45}, {1512, 1512}, {5^2*13*2^2*3^2, 5^2*13*7^2}, {51408, 51408}, {66528, 66528}, {185976, 185976}, {3^3*5^2*17*2^4*7^2, 3^3*5^2*17*2^2*13^2},....

    k=6
    {x(n), y(n)} :{5, 5}, {2^3*3^3*5^3*7^2, 2^3*3^3*5^3*7^2}, {5^3*2^2*3^2, 5^3*7^2}, {5^2*17*2^4*3^2, 5^2*17*13^2},{2^3*3^4*5^3*7^2*41, 2^3*3^4*5^3*7^2*41}, {2^10*5^4*7*41*79*157*313, 2^10*5^4*7*41*79*157*313}, ....
    Could anyone confirm them and compute more terms?


    Yasutoshi