

A097033


Number of transient terms before either 0 or a finite cycle is reached when unitaryproperdivisorsumfunction f(x) = A034460(x) is iterated and the initial value is n.


6



1, 2, 2, 2, 2, 0, 2, 2, 2, 3, 2, 3, 2, 4, 3, 2, 2, 4, 2, 4, 3, 5, 2, 4, 2, 3, 2, 4, 2, 0, 2, 2, 4, 5, 3, 5, 2, 6, 3, 5, 2, 0, 2, 3, 4, 4, 2, 5, 2, 5, 4, 5, 2, 0, 3, 3, 3, 3, 2, 0, 2, 6, 3, 2, 3, 2, 2, 6, 3, 7, 2, 5, 2, 6, 3, 5, 3, 1, 2, 6, 2, 4, 2, 6, 3, 5, 5, 5, 2, 0, 4, 5, 4, 6, 3, 6, 2, 6, 4, 1, 2, 1, 2, 6, 6
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OFFSET

1,2


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537


FORMULA

a(n) = A318883(n) + (1A318880(n)).  Antti Karttunen, Sep 23 2018


EXAMPLE

From Antti Karttunen, Sep 24 2018: (Start)
For n = 1, A034460(1) = 0 that is, we end to a terminal zero after a transient part of length 1, thus a(1) = 1.
For n = 2, A034460(2) = 1, and A034460(1) = 0, so we end to a terminal zero after a transient part of length 2, thus a(2) = 2.
For n = 30, A034460(30) = 42, A034460(42) = 54, A034460(54) = 30, thus a(30) = a(42) = a(54) = 0, as 30, 42 and 54 are all contained in their own terminal cycle, without a preceding transient part.
(End)
For n = 1506, the iterationlist is {1506, 1518, 1938, 2382, 2394, 2406, [2418, 2958, 3522, 3534, 4146, 4158, 3906, 3774, 4434, 4446, 3954, 3966, 3978, 3582, 2418, ..., ad infinitum]}. After a transient of length 6 the iteration ends in a cycle of length 14, thus a(1506) = 6.
If a(n) = 0, then n is a term in an attractor set like A002827, A063991, A097024, A097030.


PROG

(PARI)
A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))n); \\ From A034460
A097033(n) = { my(visited = Map()); for(j=1, oo, if(mapisdefined(visited, n), return(mapget(visited, n)1), mapput(visited, n, j)); n = A034460(n); if(!n, return(j))); }; \\ Antti Karttunen, Sep 23 2018


CROSSREFS

Cf. A002827, A003062, A034460, A063919, A063991, A097024, A097030, A097031, A097032A097037, A318880.
Cf. A318883 (sequence that implements the original definition of this sequence).
Sequence in context: A245476 A215884 A305029 * A268686 A113306 A181089
Adjacent sequences: A097030 A097031 A097032 * A097034 A097035 A097036


KEYWORD

nonn


AUTHOR

Labos Elemer, Aug 30 2004


EXTENSIONS

Definition corrected (to agree with the given terms) by Antti Karttunen, Sep 23 2018, based on observations by Hartmut F. W. Hoft


STATUS

approved



