A098186 -id:A098186 - cp's OEIS frontend

A098185 If f(x) = (sum of unitary proper divisors of x) = A063919(x) is iterated, the iteration may lead to a fixed point which is either equals 0 or it is from A002827, a unitary perfect number > 1: 6,60,90,87360... Here initial values are collected for which the iteration ends in a unitary perfect number > 1.

6, 60, 66, 78, 90, 244, 292, 476, 482, 578, 648, 680, 688, 770, 784, 832, 864, 956, 958, 976, 1168, 1354, 1360, 1392, 1488, 1600, 1658, 1670, 1906, 2232, 2264, 2294, 2376, 2480, 2552, 2572, 2576, 2626, 2712, 2732, 2806, 2842, 2870, 2904, 2912, 2992, 3024

Offset: 1

Labos Elemer, Aug 31 2004

nonn

			Initial values attracted by 87360 (4th unitary perfect number) are collected separately in A098186.
It seems that 6 is the only initial value ending in fixed point = 6.

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A063919, A002827, A063991, A097024, A097030-A097037.

di[x_] :=Divisors[x];ta={{0}}; ud[x_] :=Part[di[x],Flatten[Position[GCD[di[x],Reverse[di[x]]],1]]]; asu[x_] :=Apply[Plus,ud[x]]-x;nsf[x_,ho_] :=NestList[asu,x,ho] Do[g=n;s=Last[NestList[asu,n,100]]; If[Equal[s,6]||Equal[s,60]||Equal[s,90],Print[{n,s}]; ta=Append[ta,n]],{n,1,256}];ta = Delete[ta,1]

A098188 Irregular triangle with 4 columns which contains in each row the members of a 4-cycle under the map x->A063919(x), iteration of summing the proper-unitary divisors.

Original entry on oeis.org

263820, 263940, 280380, 280500, 395730, 395910, 420570, 420750, 172459210, 218725430, 272130250, 218628662, 209524210, 246667790, 231439570, 230143790, 384121920, 384296640, 408233280, 408408000

Offset: 1

Labos Elemer, Sep 02 2004

Initial values attracted by this sequence are in A098187.

The iteration of this function also contains 2-cycles like 114->126->114... or 1140 -> 1260 ->1140,... or 3-cycles like 30->42->54->30->....

			The first line represents the 4-cycle  280500->263820->263940->280380->280500->...,
The second line represents the 4-cycle 420750->395730->395910->420570->420750->..

J. O. M. Pedersen, Known Unitary Sociable Numbers of order four [Via Internet Archive Wayback-Machine]
J. O. M. Pedersen, Order 4 cycles, 2007.
Eric Weisstein's World of Mathematics, Unitary Sociable Numbers

Cf. A098185, A098186, A002827, A097024, A097030, A098187.

Cf. A319902 (where the terms are entered by increasing value).

More terms from Michel Marcus, Oct 05 2018

A098187 Initial seeds x which will enter a cycle of length 4 under the iteration of x -> A063919(x), the sum of proper unitary divisors.

Original entry on oeis.org

81570, 114270, 137046, 169998, 177906, 182082, 182094, 185190, 194574, 194586, 201642, 203442, 204420, 204540, 212466, 212874, 213870, 219306, 219318, 230874, 231438, 231834, 231846, 232626, 237678, 238134, 242634, 258882, 259338, 259350

Offset: 1

Labos Elemer, Sep 02 2004

nonn

The sequence is the attractor-basin of set of {C4} cycles belonging to this iteration.

The {C4} attractor-set is displayed separately in A098188.

			81570 is in the sequence because its track under the iterated map is 81570, 114270, 182082, 182094, 232626, 237678, 305682, 352878, 360978, 403662, 420738, [420750, 395730, 395910, 420570], 420750.., where the cycle is indicated by brackets. The 4 recurrent terms appear after 11 transients for this case.

Cf. A098185, A098186, A002827, A097024, A097030.

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A098188 Irregular triangle with 4 columns which contains in each row the members of a 4-cycle under the map x->A063919(x), iteration of summing the proper-unitary divisors.

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A098187 Initial seeds x which will enter a cycle of length 4 under the iteration of x -> A063919(x), the sum of proper unitary divisors.

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