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

Author

Ant King, Jan 24 2007

Keywords

• hard
• nonn

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.

Examples

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

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

• 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.

Crossrefs

Cf. A127161, A127162, A127163, A127164, A063769, A063990, A097032, A098007, A097010, A127653, A098185, A127654, A063991, A127655, A097037, 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]];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[ # ]] &]

Formula

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