A290143 Numbers n such that transient part of the unitary aliquot sequence for n sets a new record.

1, 2, 10, 14, 22, 38, 70, 134, 138, 170, 190, 210, 318, 426, 1398, 4170, 6870, 8454, 19866, 22470, 36282, 38370, 70770, 84774, 98790, 132990, 474642, 705990, 961650

Offset

1,2

Comments

The unitary version of A098009.

The record values are in A290144.

References

Richard K. Guy, "Unitary aliquot sequences", Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004. B8, pp. 97-99.

Richard K. Guy and Marvin C. Wunderlich, Computing Unitary Aliquot Sequences: A Preliminary Report, University of Calgary, Department of Mathematics and Statistics, 1979.

H. J. J. te Riele, Unitary Aliquot Sequences, MR 139/72, Mathematisch Centrum, 1972, Amsterdam.

H. J. J. te Riele, Further Results On Unitary Aliquot Sequences. NW 2/73, Mathematisch Centrum, 1973, Amsterdam.

Links

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Unitary Aliquot Sequence

Example

The unitary aliquot sequence of 134 is: 134, 70, 74, 40, 14, 10, 8, 1. Its length is 8 and it is longer than the unitary aliquot sequences of all the numbers below 134.

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];
g[n_] := If[n > 0, usigma[n] - n, 0]; f[n_] := NestWhileList[g, n, UnsameQ, All]; a = -1; seq = {}; Do[b = Length[f[n]] - 1; If[b > a, a = b; AppendTo[seq, n]], {n, 10^6}] ; seq (* after Giovanni Resta at A034448 & Robert G. Wilson v at A098009 *)

Crossrefs

Cf. A098008, A098009, A098010, A127652, A127653, A127654, A127655, A290144.

Sequence in context: A349833 A091999 A230624 * A160773 A217191 A190043

Adjacent sequences: A290140 A290141 A290142 * A290144 A290145 A290146

Keyword

nonn,more

Author

Amiram Eldar, Jul 21 2017

Status

approved