A098195 Starting values x such that the map x -> A098189(x) enters any cycle of length 29.

246, 250, 274, 276, 278, 282, 345, 356, 382, 386, 390, 392, 399, 400, 405, 424, 438, 468, 474, 478, 482, 484, 486, 490, 510, 522, 524, 534, 556, 562, 566, 570, 578, 579, 591, 594, 598, 602, 614, 618, 620, 621, 622, 626, 628, 630, 642, 645, 648, 650, 662

Offset: 1

Author

Labos Elemer, Sep 03 2004

Keywords

• nonn

Comments

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.

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

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

Examples

			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
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

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 *)

Formula

{x: A098190(x) = 29}.

Extensions

Edited by R. J. Mathar, May 15 2009