[seqfan] Re: Generalized Amicable Number

[Jack Brennen]

For your first pair, it seems that they satisfy the equation:

    (-1)Sigma(x)=(-1)Sigma(y)=4/3*(x*y)^(1/2)

I can confirm that the other two you provided are correct.

Is it possible that the ratio of 8/5 doesn't need to be
fixed, but instead of the form 2-2/p ?  Given the significance
of the "-2" in the computation of (-1)Sigma(x), I could imagine
how that might make sense.

Pairs that I found that satisfy the equation at the given 8/5
ratio include:

x = y = 2^3*3^3*5*13*19

x = 3^3*7*19*29*2^4
y = 3^3*7*19*29*5^2           {Your 3rd pair}

x = y = 2^4*3^3*5*7*19*29
x = y = 2^2*3^3*5^2*7*19*29   {Your 2nd pair}
x = y = 2^2*3^3*5^3*7*11*19
x = y = 2^6*3*5^5*61
x = y = 2^3*3^2*5^2*7*11*13*29


On 2/8/2015 10:43 PM, zbi74583.boat at orange.zero.jp wrote:
>      Hi,Seqfans
>      I genaralized Amicable Number as follows
>
>      (-1)Sigma(x)=(-1)Sigma(y)=8/5*(x*y)^(1/2)
>
>      The definition of (-1)Sigma(x) is here A049060
>
>      I computed it by hand
>
>      x = 5^2*11*29*2^2*3^2
>      y = 5^2*11*29*7^2
>
>      x = y
>        = 2^2*3^3*5^2*7*19*29
>
>      x = 3^3*7*19*29*2^4
>      y = 3^3*7*19*29*5^2
>
>      Could anyon confirm them and compute
>      more term?
>
>
>
>      Yasutoshi
>
>
>
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