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

1,1

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]

Example

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

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[ # ]]] &]

Crossrefs

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

Sequence in context: A204867 A204860 A277459 * A206659 A206652 A158127

Adjacent sequences: A127652 A127653 A127654 * A127656 A127657 A127658

Keyword

nonn

Author

Ant King, Jan 25 2007

Extensions

More terms from Amiram Eldar, Apr 06 2019

Status

approved