another aliquot 2

[y.kohmoto]

    Hello, sequfans.
    [another kind of aliquot sequence]

    The sequence which is defined as follows is called (-1)sigma sequence :

    a(n)=(-1)sigma(a(n-1))

　　If x=Product p_i^r_i,
　　then (-1)sigma(x)=Product (-1+Sum p_i^s_i, s_i=1 to r_i)
A049060
　　Ex.
　　　　 (-1)sigma(24)=(-1+2+4+8)*(-1+3)=1-2-4-8-3+6+12+24
　　　　 all terms are divisors of 24, but it is not the sum of divisors.
　　　　 It is a difference of divisors.

    Two cases are possible :
    1. It becomes cyclic.
    2. It becomes divergent.
    If the sequence becomes a cyclic sequence, then it is called a (-1)sigma
sociable number of order k.
    k is number of the members.

    The longest record of (-1)sigma sociable number.

    k=8
    2^3*5*7*29 - 2^5*3*7*13 - 2^4*3^2*61 - 2^2*3*5*11*29 -
2^6*5^2*7 -2*3*5^3*29 - 2^4*7^2*11 - 2*5^2*11*29
    k=8
    2^6*3*5^2 - 2*5^3*29 - 2^3*7^2*11 - 2*5^2*11*13 - 2^3*3*5*29 -2^5*7*13 -
2^3*3^2*61 - 2^2*3*5*11*13　　

    I know no mathematician who studies this sequence.
    Tell me any discovery about it.

    Yasutoshi

    http://boat.zero.ad.jp/~zbi74583/another02.htm