A008888 Aliquot sequence starting at 138.

138, 150, 222, 234, 312, 528, 960, 2088, 3762, 5598, 6570, 10746, 13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754, 40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812, 2109796, 1889486, 953914, 668966, 353578, 176792

Offset

0,1

Comments

The sum-of-divisor function A000203 and aliquot parts A001065 are defined only for positive integers, so the trajectory ends when 0 is reached, here at index 178. - M. F. Hasler, Feb 24 2018

Merges into sequence A008889 after the first step.

References

R. K. Guy, Unsolved Problems in Number Theory, B6.

Enoch Haga, Exploring Prime Numbers on Your PC, 2nd ed., 1998, pages 83-84 and Table 8, page 46. ISBN 1-885794-16-9.

Links

T. D. Noe, Table of n, a(n) for n = 0..178 (full sequence).

Christophe Clavier, Aliquot Sequences

Passawan Noppakaew and Prapanpong Pongsriiam, Product of Some Polynomials and Arithmetic Functions, J. Int. Seq. (2023) Vol. 26, Art. 23.9.1.

Index entries for sequences related to aliquot parts.

Formula

a(n) = A001065(a(n-1)) for n > 0, thus a(n) = A001065^n(138) for all n < 179. - M. F. Hasler, Nov 16 2013

a(n) = A008889(n-1) for all n >= 1. - M. F. Hasler, Feb 24 2018

Maple

f := proc(n) option remember; if n = 0 then 138; else sigma(f(n-1))-f(n-1); fi; end:

Mathematica

FixedPointList[If[# > 0, DivisorSigma[1, #] - #, 0]&, 138] // Most (* Jean-François Alcover, Mar 28 2020 *)

Prog

(PARI) a(n, a=138)={for(i=1, n, a=sigma(a)-a); a} \\ M. F. Hasler, Feb 24 2018

Crossrefs

Cf. A008885 (starting at 30), ..., A008892 (starting at 276), A098007 (length of aliquot sequences).

Sequence in context: A031964 A114820 A107939 * A045045 A108156 A264897

Adjacent sequences: A008885 A008886 A008887 * A008889 A008890 A008891

Keyword

nonn,fini,full

Author

N. J. A. Sloane.

Extensions

Term 179 removed from b-file by Ivan Panchenko, Nov 16 2013

Edited by M. F. Hasler, Feb 24 2018

Status

approved