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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
OFFSET
1,1
LINKS
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]
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 31 2004
STATUS
approved