[seqfan] Re: Generalized Amicable Number

[zbi74583.boat at orange.zero.jp]

    Hi,Jack
    Thank you for confirming and computing more terms

    The first number was the following

    x = 5^3*11^2*13*131*2^2*3^2
    y = 5^3*11^2*13*131*7^2

    I am sorry that I wrote a wrong number which I wrote on next line in my note
book
    Could you confirm it?



    I am now computing the numbers which satisfy the following

    F(x)=F(y)=m/n*(x*y)^(1/2)

    Where F(k) is one of the divisor function, both m,n are small

    Here is an interesting example

    UnitaryPhi(x)=UnitaryPhi(y)=m/n*(x*y)^(1/2)

    m/n=3/4    A143649
    x = 2^10*5*3^2*11^2
    y = 2^10*5*31^2
    Is it tenth term?

    m/n=4/5
    x = y = 5

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

    x = 5^4*7*2^10*3^8*11^2*41^2
    y = 5^4*7*2^20*3^2*13^2*31^2

    Could you confirm them and compute more terms?



    >(-1)Sigma(x)=(-1)Sigma(y)=8/5*(x*y)^(1/2)

    >The definition of (-1)Sigma(x) is here A049060



    Yasutoshi