[seqfan] Please help me describe this sequence

[Christian Lawson-Perfect]

Hi seqfans,
I've come up with a new sequence, but I'm not sure how best to describe it
in an OEIS entry.

It arises from a dynamical process. You start with a natural number N, and
a total T that starts at 0. At each step, do this:

* if N is 1, stop
* add N to T
* if N divides T, add 1 to N, otherwise subtract 1 from N.

So the sequence of N and T might look like this, for starting N = 4:

N	T
4	0
5	4
4	9
3	13
2	16
3	18
4	21
...	...


Or this, for starting N = 8:

N	T
8	0
9	8
8	17
7	25
6	32
5	38
4	43
3	47
2	50
3	52
2	55
1	57
stop

I always have trouble filling in the short description field for OEIS
entries. Can anyone help?