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A003062
Beginnings of periodic unitary aliquot sequences.
(Formerly M4190)
8
6, 30, 42, 54, 60, 66, 78, 90, 100, 102, 114, 126, 140, 148, 194, 196, 208, 220, 238, 244, 252, 274, 288, 292, 300, 336, 348, 350, 364, 374, 380, 382, 386, 388, 400, 420, 436, 440, 476, 482, 484, 492, 516, 528, 540, 542, 550, 570, 578, 592, 600, 612, 648, 660, 680, 688, 694, 708, 720, 722, 740, 756, 758, 764, 766, 770, 780, 784, 792, 794, 812
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
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;
A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
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
Cf. A034460, A097010 (complement), A318880 (characteristic function).
Sequence in context: A151711 A130512 A127662 * A327157 A336216 A309312
KEYWORD
nonn
EXTENSIONS
More terms from Antti Karttunen, Sep 23 2018
STATUS
approved