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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
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
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[ # ]] &]
KEYWORD
hard,nonn
AUTHOR
Ant King, Jan 24 2007
STATUS
approved