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 A097033 Number of transient terms before either 0 or a finite cycle is reached when unitary-proper-divisor-sum-function 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A318883(n) + (1-A318880(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 iteration-list 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, A097032-A097037, 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

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Last modified May 17 09:03 EDT 2021. Contains 343969 sequences. (Running on oeis4.)