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A127652 Integers whose unitary aliquot sequences are longer than their ordinary aliquot sequences. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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

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.

Creyaufmueller, Wolfgang, 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 A259028 A317392

Adjacent sequences:  A127649 A127650 A127651 * A127653 A127654 A127655

KEYWORD

hard,nonn

AUTHOR

Ant King, Jan 24 2007

STATUS

approved

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Last modified April 5 09:06 EDT 2020. Contains 333238 sequences. (Running on oeis4.)