A127655 Numbers whose unitary aliquot sequences end in a unitary amicable pair, but which are not unitary amicable numbers themselves.

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

Offset: 1

Author

Ant King, Jan 25 2007

Keywords

• nonn

Examples

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

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]
• J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]
• J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]

Crossrefs

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

Programs

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[ # ]]] &]

Extensions

More terms from Amiram Eldar, Apr 06 2019