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Starting values x such that the map x -> A098189(x) enters any cycle of length 29.
7

%I #11 Mar 02 2017 23:05:57

%S 246,250,274,276,278,282,345,356,382,386,390,392,399,400,405,424,438,

%T 468,474,478,482,484,486,490,510,522,524,534,556,562,566,570,578,579,

%U 591,594,598,602,614,618,620,621,622,626,628,630,642,645,648,650,662

%N Starting values x such that the map x -> A098189(x) enters any cycle of length 29.

%C Iterating the map x -> A098189(x) may enter a cycle with 29 members (and there may be distinct cycles each with 29 members). The sequence lists all starting values of x such that (after some transient x) one of these cycles of length 29 is entered.

%C See other attractors and basins of attracted terms in A098191-A098195.

%C Corresponding number of transient terms for each term in a(n): {26, 25, 25, 25, 24, 23, 25, 26, 23, 22, 21, 24, 26, 24, 26, 25, 22, 27, 39, 17, 16, 22, 15, 27, 22, 27, 25, 25, 26, 16, 15, 14, 23, 25, 25, 33, 22, 39, 14, 13, 34, 26, 16, 15, 18, 14, 23, 34, 28, 20, 23, ...}. - _Michael De Vlieger_, Mar 01 2017

%H Michael De Vlieger, <a href="/A098195/b098195.txt">Table of n, a(n) for n = 1..1000</a>

%F {x: A098190(x) = 29}.

%e 282 is in the sequence since iterating the map x -> A098189(x) on that number yields 23 transient terms {282, 484, 390, 912, 1072, 628, 478, 482, 486, 570, 1296, 962, 1164, 1576, 998, 1002, 1684, 1270, 1800, 1860, 3360, 5568, 6008} then enters a cycle of 29 terms {3768, 4440, 7056, 6484, 4870, 6840, 9072, 8560, 7624, 4778, 4782, 7984, 4516, 3394, 3398, 3402, 4884, 7680, 10264, 6428, 4828, 4240, 3844, 2950, 3520, 3400, 2932, 2206, 2210}. - _Michael De Vlieger_, Mar 01 2017

%t Lookup[#, 29] &@ PositionIndex@ #[[All, -1]] &@ Table[If[n == 1, {0, 1}, Function[s, Function[t, {#, First@ Differences@ Take[Flatten@ t[[# + 1]], 2]} &@ Count[DeleteDuplicates@ t, k_ /; Length@ k == 1]]@ Map[Position[s, #] &, s]]@ NestList[Function[n, DivisorSum[n, # &, CoprimeQ[#, n/#] &] - EulerPhi@ n], n, n + 120]], {n, 800}] (* _Michael De Vlieger_, Mar 01 2017, Version 10 *)

%Y Cf. A063919, A098189, A098190, A098191, A098192, A098193, A098194.

%K nonn

%O 1,1

%A _Labos Elemer_, Sep 03 2004

%E Edited by _R. J. Mathar_, May 15 2009