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A127655
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Numbers whose unitary aliquot sequences end in a unitary amicable pair, but which are not unitary amicable numbers themselves.
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1
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102, 388, 436, 484, 812, 866, 1020, 1036, 1040, 1116, 1196, 1380, 1500, 1524, 1532, 1552, 1618, 1644, 1716, 1724, 1726, 1744, 1916, 2020, 2066, 2068, 2324, 2368, 2386, 2486
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| Riele, H. J. J. te; Unitary Aliquot Sequences. MR 139/72, Mathematisch Centrum, 1972, Amsterdam.
Riele, H. J. J. te; Further Results On Unitary Aliquot Sequences. NW 2/73, Mathematisch Centrum, 1973, Amsterdam.
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LINKS
| Pederse, Jan Munch, Tables Of Aliquot Cycles,
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EXAMPLE
| a(5)=812 because the fifth non unitary amicable number whose unitary aliquot sequence ends in a unitary amicable pair is 812.
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MATHEMATICA
| UnitaryDivisors[n_Integer?Positive]:=Select[Divisors[n], GCD[ #, n/# ]==1&]; sstar[n_]:=Plus@@UnitaryDivisors[n]-n; g[n_] := If[n > 0, sstar[n], 0]; UnitaryTrajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]]; UnitaryAmicableNumberQ[k_]:=If[Nest[sstar, k, 2]?k && !sstar[k]?k, True, False]; Select[Range[2500], !UnitaryAmicableNumberQ[ # ] && UnitaryAmicableNumberQ[Last[UnitaryTrajectory[ # ]]] &]
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CROSSREFS
| Cf. A063991, A097037, A127654, A098185, A097032, A097010, A127653, A097036.
Sequence in context: A203407 A204867 A204860 * A206659 A206652 A158127
Adjacent sequences: A127652 A127653 A127654 * A127656 A127657 A127658
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KEYWORD
| hard,nonn
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AUTHOR
| Ant King (mathstutoring(AT)ntlworld.com), Jan 25 2007
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