# another aliquot 2

Fri Apr 25 03:19:53 CEST 2003

```    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

```