A127652 Integers whose unitary aliquot sequences are longer than their ordinary aliquot sequences.

25, 28, 36, 40, 50, 68, 70, 74, 94, 95, 98, 116, 119, 134, 142, 143, 154, 162, 170, 175, 182, 189, 190, 200, 220, 226, 242, 245, 262, 273

Offset

1,1

Comments

Here the length of an aliquot sequence is defined to be the length of the transient part of its trajectory + the length of its terminal cycle.

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

Table of n, a(n) for n=1..30.

Manuel Benito and Juan L. Varona, Advances In Aliquot Sequences, Mathematics of Computation, Vol. 68, No. 225, (1999), pp. 389-393.

Wolfgang Creyaufmueller, Aliquot Sequences.

Formula

Sequence gives those values of n for which A097032(n)>A098007(n).

Example

a(5)=50 because the fifth integer whose unitary aliquot sequence is longer than its ordinary aliquot sequence is 50.

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]]; s[n_]:=DivisorSigma[1, n]-n; h[n_] := If[n > 0, s[n], 0]; OrdinaryTrajectory[n_] := Most[NestWhileList[h, n, UnsameQ, All]]; Select[Range[275], Length[UnitaryTrajectory[ # ]]>Length[OrdinaryTrajectory[ # ]] &]

Crossrefs

Cf. A127161, A127162, A127163, A127164, A063769, A063990, A097032, A098007, A097010, A127653, A098185, A127654, A063991, A127655, A097037, A097036.

Sequence in context: A295748 A254226 A195613 * A303812 A334534 A259028

Adjacent sequences: A127649 A127650 A127651 * A127653 A127654 A127655

Keyword

hard,nonn

Author

Ant King, Jan 24 2007

Status

approved