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A291789 Trajectory of 270 under repeated application of k -> (phi(k)+sigma(k))/2. 7
270, 396, 606, 712, 851, 852, 1148, 1416, 2032, 2488, 2960, 4110, 5512, 6918, 8076, 10780, 16044, 23784, 33720, 55240, 73230, 97672, 118470, 169840, 247224, 350260, 442848, 728448, 1213440, 2124864, 4080384, 8159616, 13515078, 15767596, 18626016, 29239504, 39012864, 62623600, 92580308 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The ultimate fate of this trajectory is presently unknown. It may reach a fractional value (when it dies), it may reach a prime (which would be a fixed point), it may enter a cycle of length greater than 1, or it may be unbounded. - Hugo Pfoertner and N. J. A. Sloane, Sep 18 2017
LINKS
Sean A. Irvine, Table of n, a(n) for n = 0..515 [Terms through a(250) from Hugo Pfoertner, terms a(251)-a(356) from N. J. A. Sloane]
N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 14.
MAPLE
orbit:= proc(n, m) uses numtheory;
local V, k;
V:= Vector(m);
V[1]:= n;
for k from 2 to m do V[k]:= (sigma(V[k-1])+ phi(V[k-1]))/2 od:
convert(V, list)
end proc:
orbit(270, 200); # Robert Israel, Sep 07 2017
MATHEMATICA
NestWhileList[If[! IntegerQ@ #, -1/2, (DivisorSigma[1, #] + EulerPhi@ #)/2] &, 270, Nor[! IntegerQ@ #, SameQ@ ##] &, 2, 38] (* Michael De Vlieger, Sep 19 2017 *)
CROSSREFS
See A291914 and A292108 for the "big picture".
Sequence in context: A291790 A025394 A345173 * A292766 A180151 A278130
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 03 2017
STATUS
approved

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Last modified March 19 07:25 EDT 2024. Contains 370955 sequences. (Running on oeis4.)