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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. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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.

MATHEMATICA

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]

CROSSREFS

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

Sequence in context: A237576 A229097 A217399 * A173904 A308413 A204093

Adjacent sequences:  A098182 A098183 A098184 * A098186 A098187 A098188

KEYWORD

nonn

AUTHOR

Labos Elemer, Aug 31 2004

STATUS

approved

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Last modified September 22 21:07 EDT 2020. Contains 337291 sequences. (Running on oeis4.)