OFFSET
1,1
COMMENTS
Provided that A034460 has no infinite unbounded trajectories, these are also numbers m such that when iterating the map k -> A034460(k), starting from k = m, the iteration will never reach 0, that is, will instead eventually enter into a finite cycle. - Antti Karttunen, Sep 23 2018
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
H. J. J. Te Riele, Unitary Aliquot Sequences, Report MR-139/72, Mathematisch Centrum, Amsterdam, September 1972.
MATHEMATICA
a034460[0] = 0; (* avoids dividing by 0 when an iteration reaches 0 *)
a034460[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/; n>0
periodicQ[k_] := NestWhile[a034460, k, UnsameQ, All]!=0
nmax = 812; Select[Range[nmax], periodicQ]
(* Hartmut F. W. Hoft, Jan 24 2024 *)
PROG
(PARI)
up_to = 20000;
A318880(n) = { my(visited = Map()); for(j=1, oo, if(mapisdefined(visited, n), return(1), mapput(visited, n, j)); n = A034460(n); if(!n, return(0))); };
A003062list(up_to) = { my(v = vector(up_to), k=0, n=1); while(k<up_to, if(A318880(n), k++; v[k] = n); n++); (v); };
v003062 = A003062list(up_to);
A003062(n) = v003062[n]; \\ Antti Karttunen, Sep 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Antti Karttunen, Sep 23 2018
STATUS
approved