A003062 Beginnings of periodic unitary aliquot sequences. (Formerly M4190)

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

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;
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).

Cf. also A002827, A063991, A097024, A097030, A097034, A097035, A097036, A097037.

Sequence in context: A151711 A130512 A127662 * A327157 A336216 A309312

Adjacent sequences: A003059 A003060 A003061 * A003063 A003064 A003065

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Antti Karttunen, Sep 23 2018

Status

approved