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A008888 Aliquot sequence starting at 138. 9
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 (list; graph; refs; listen; history; text; internal format)
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.
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
KEYWORD
nonn,fini,full
AUTHOR
EXTENSIONS
Term 179 removed from b-file by Ivan Panchenko, Nov 16 2013
Edited by M. F. Hasler, Feb 24 2018
STATUS
approved

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Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)