[seqfan] defn of A032452 transients in modified Poulet

[Richard J. Mathar]

It would be nice to have a definition of a(n) in terms of n in A032452 (modified Poulet sequences).
Starting at n, we have the sequences
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...], 
[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...], 
[3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
[4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...], 
[5, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...], 
[6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...],
[7, 6, 2, 3, 2, 1, 1, 1, 1, 1, 1,...], 
[8, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...], 
[9, 6, 2, 3, 2, 1, 1, 1, 1, 1, 1,...],
[10, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...]
[11, 10, 4, 7, 6, 2, 3, 2, 1, 1, 1,...]
[12, 4, 2, 3, 2, 1, 1, 1, 1, 1, 1,...]
[13, 12, 4, 7, 6, 2, 3, 2, 1, 1, 1,...]
...
if we iterate twice phi(.) and once sigma(.) on the elements in these sequences.
I suspect that a(n) is somehow a cumulation of periods or their transients,
similar to A032450, but cannot find how that might actually be realized in A032452.