[seqfan] Re: Add to an integer its distinct factors and loop

[franktaw at netscape.net]

From: Eric Angelini <Eric.Angelini at kntv.be>

Hello SeqFans,

>"Add to an integer N its distinct factors and loop"
Choose one of the factorizations of N into two or more distinct factors 
each greater than 1, add those factors to N and loop

>...
>12-->2*6--->20-->2*10-->32-->4*8--->44-->2*22-->68-->2*34-->104-->...
>...

This particular sequence must end shortly after this.  There are 4 
possibilities:

104 -> 123 -> 167.
104 -> 125 -> 155 -> 191.
104 -> 134 -> 203 -> 239.
104 -> 158 -> 239.

However, I am fairly sure that there are infinite sequences.  Starting 
with 48, we can get:

48 -> 64 -> 84 -> 128 -> 152 -> 230 -> 260 -> 392 -> 590 -> 656 -> 824 
-> 935 -> 968 -> 1454 -> 2183 -> 2279 -> 2375 -> 2424 -> 2634 -> 3078 
-> ...

Having gotten up into the range where the number of factors is usually 
fairly large, it should always be possible to find a path forward, with 
only the occasional back and fill.

Franklin T. Adams-Watters