From: PMA98DAV@shef.ac.uk (D A S Vivash)
Subject: Re: Watercat analysis
Date: 26 Jan 1999 19:44:37 GMT
Newsgroups: sci.math
Keywords: Sociable numbers (sum of divisors function)

In article <36AE0EA4.A27AF3B2@dd.chalmers.se>, gu96magi@dd.chalmers.se says...
>
>Look at the sequence:
>
>N1, N2, N3, ......
>
>where N1 is any integer, and N(k+1) is the sum of the proper divisors of
>N(k).
>
>1) Are there any sequences which are periodic, with period larger than
>two?

I just looked at http://xraysgi.ims.uconn.edu:8080/amicable.html
Look at the section under "Sociable numbers"

Apparantly, and I quote "There are 53 cycles in all: 46 of 
length 4, 1 of length 5, 2 of length 6, 2 of length 8, 1 of length 9, and 1 
of length 28."

>2) Are there any sequences which tend to infinity?

Probably

>3) Are there any sequences, such that [the number of terms in the
>sequence, before it turns to 1] equals N0?
>4) Are there any really large sequences?



David