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A008888 Aliquot sequence starting at 138. 9

%I #42 Nov 17 2023 11:49:50

%S 138,150,222,234,312,528,960,2088,3762,5598,6570,10746,13254,13830,

%T 19434,20886,21606,25098,26742,26754,40446,63234,77406,110754,171486,

%U 253458,295740,647748,1077612,1467588,1956812,2109796,1889486,953914,668966,353578,176792

%N Aliquot sequence starting at 138.

%C 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

%C Merges into sequence A008889 after the first step.

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

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

%H T. D. Noe, <a href="/A008888/b008888.txt">Table of n, a(n) for n = 0..178</a> (full sequence).

%H Christophe Clavier, <a href="http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html">Aliquot Sequences</a>

%H Passawan Noppakaew and Prapanpong Pongsriiam, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Pongsriiam/pong43.html">Product of Some Polynomials and Arithmetic Functions</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.9.1.

%H <a href="/index/Al#ALIQUOT">Index entries for sequences related to aliquot parts</a>.

%F 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

%F a(n) = A008889(n-1) for all n >= 1. - _M. F. Hasler_, Feb 24 2018

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

%t FixedPointList[If[# > 0, DivisorSigma[1, #] - #, 0]&, 138] // Most (* _Jean-François Alcover_, Mar 28 2020 *)

%o (PARI) a(n,a=138)={for(i=1,n,a=sigma(a)-a);a} \\ _M. F. Hasler_, Feb 24 2018

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

%K nonn,fini,full

%O 0,1

%A _N. J. A. Sloane_.

%E Term 179 removed from b-file by _Ivan Panchenko_, Nov 16 2013

%E Edited by _M. F. Hasler_, Feb 24 2018

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)