A141059 and Quadratic Amicable

[koh]

    Hi,Seqfans


    I considered about the regular type of solution of Quadratic Amicable Number.
         UnitarySigma(x) = UnitarySigma(y) = 1/k*(x^2+m*y^2)/(x+y)
         k<x<y

         If 
         x=c*u
         y=c*v
         GCD(c,u)=1, GCD(c,v)=1
         Then c is called "Sprout", {u,v} is called "Seed".
         {x,y} is called "Regular type".

         k=((u-v)*(1-v)+i*v^2)*c/UnitarySigma(c)
         m=(u-v)*(u+v)-1 + i*(u+v)*(1+v)

         c ｍust satisfy the following conditions.

         (u-v)*(1-v)+i*v^2 = 0 Mod UnitalySigma(c) , 0<=i 
         (u-v)*(1-v)+i*v^2 < c*u
         GCD(c,u)=1, GCD(c,v)=1

         So, {number of the sprout of seed {u,v} for eadh i} < A141059(((u-v)*(1-v)+i*v^2)

         {u,v}={6,11} It is the smallest seed.

         c = 7^2,419....

         {u,v)={10,17}

         c = 13,3^3,137,229,....

         {u,v}={12,19}

         c = 41,5^3,....

         {u,v}={15,23}

         c = 43,....

         {u,v}={18,29}

         c = 43,307,....

         {u,v]={20,29]

         c = 17,3^3,41,251,....

         {u,v}={21,31}

         c = 19,2^2*5,29,2*19,2^2*11,59,2^2*29,149,2^2*59,....

         Sequence of Quadratic Amicable Number.

         x :
         130,270,294,340,399,420,492,540,609,645, 774, 798, 820, 924,1239,1370

         y :
         221,459,539,493,589,620,779,783,899,989,1247,1178,1189,1364,1829,2328            
    It is difficult to get irregular type by hand.
    Could anyone search them using a computer?

    To Neil

    Do x,y fit to OEIS?




    Yasutoshi