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

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

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.

Crossrefs

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

Programs

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 *)

PARI

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

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

Extensions

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

Edited by M. F. Hasler, Feb 24 2018