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Numbers whose unitary aliquot sequences end in a unitary amicable pair, but which are not unitary amicable numbers themselves.
5

%I #16 Apr 06 2019 06:35:46

%S 102,388,436,484,812,866,1020,1036,1040,1116,1196,1380,1500,1524,1532,

%T 1552,1618,1644,1716,1724,1726,1744,1916,2020,2066,2068,2324,2368,

%U 2386,2486,2592,2684,2880,2924,3032,3098,3120,3124,3136,3276,3400,3442,3444,3446,3482

%N Numbers whose unitary aliquot sequences end in a unitary amicable pair, but which are not unitary amicable numbers themselves.

%D Riele, H. J. J. te; Unitary Aliquot Sequences. MR 139/72, Mathematisch Centrum, 1972, Amsterdam.

%D Riele, H. J. J. te; Further Results On Unitary Aliquot Sequences. NW 2/73, Mathematisch Centrum, 1973, Amsterdam.

%H Amiram Eldar, <a href="/A127655/b127655.txt">Table of n, a(n) for n = 1..1000</a>

%H J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Broken link]

%H J. O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Via Internet Archive Wayback-Machine]

%H J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a> [Cached copy, pdf file only]

%e a(5)=812 because the fifth non-unitary amicable number whose unitary aliquot sequence ends in a unitary amicable pair is 812.

%t 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[ # ]]] &]

%Y Cf. A063991, A097037, A127654, A098185, A097032, A097010, A127653, A097036.

%K nonn

%O 1,1

%A _Ant King_, Jan 25 2007

%E More terms from _Amiram Eldar_, Apr 06 2019