OFFSET
1,2
COMMENTS
Suggested by N. J. A. Sloane in a post "Iterating some number-theoretic functions" to the Seqfan mailing list.
The iteration arrives at a fixed point when k becomes a prime P, because sigma(P)=P+1 and phi(P)=P-1, hence k -> k.
It would be nice to have an independent characterization of these numbers (not involving the map in the definition). - N. J. A. Sloane, Sep 03 2017
Conjecturally, all terms of A291790 are in the sequence, because their trajectories (see example in A291789 for starting value 270) grow indefinitely. - Hugo Pfoertner, Sep 04 2017
LINKS
N. J. A. Sloane, Iterating some number-theoretic functions, Posting in Seqfan mailing list, Sep 3, 2017
EXAMPLE
126 is in the sequence, because the following iteration arrives at a fixed point:
k sigma(k) phi(k)
126 312 36 k->(sigma(k)+phi(k))/2, (312+36)/2=174
174 360 56 k->(sigma(k)+phi(k))/2, (360+56)/2=208
208 434 96
265 324 208
266 480 108
294 684 84
384 1020 128
574 1008 240
624 1736 192
964 1694 480
1087 1088 1086 k->(sigma(k)+phi(k))/2, (1088+1086)/2=1087
1087 1088 1086 ... loop
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Sep 03 2017
STATUS
approved