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A008892 Aliquot sequence starting at 276.

%I A008892 #87 Mar 15 2025 17:34:49
%S A008892 276,396,696,1104,1872,3770,3790,3050,2716,2772,5964,10164,19628,
%T A008892 19684,22876,26404,30044,33796,38780,54628,54684,111300,263676,465668,
%U A008892 465724,465780,1026060,2325540,5335260,11738916,23117724,45956820,121129260,266485716
%N A008892 Aliquot sequence starting at 276.
%C A008892 It is an open question whether this sequence ever reaches 0. The trajectory has been calculated to 2145 terms, and is still growing, term 2145 being a 214-digit number (see FactorDB link). - _N. J. A. Sloane_, Jan 11 2023
%C A008892 The aliquot sequence starting at 306 joins this sequence after one step.
%C A008892 This sequence cannot be extended backwards, since A359132(276) = -1. - _N. J. A. Sloane_, Jan 10 2023
%C A008892 One can note that the k-tuple abundance of 276 is only 5, since a(6) = 3790 is deficient. On the other hand, the k-tuple abundance of a(8) = 2716 is 164 since a(172) is deficient (see A081705 for definition of k-tuple abundance). - _Michel Marcus_, Dec 31 2013
%D A008892 K. Chum, R. K. Guy, M. J. Jacobson, Jr., and A. S. Mosunov, Numerical and statistical analysis of aliquot sequences. Exper. Math. 29 (2020), no. 4, 414-425; arXiv:2110.14136, Oct. 2021 [math.NT].
%D A008892 Richard K. Guy, Unsolved Problems in Number Theory, B6.
%D A008892 Richard K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.
%H A008892 Tyler Busby, <a href="/A008892/b008892.txt">Table of n, a(n) for n = 0..2157</a> (terms 0..2127 from Daniel Suteu, terms 2128..2140 from Jeppe Stig Nielsen)
%H A008892 Christophe Clavier, <a href="http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html">Aliquot Sequences</a>
%H A008892 Christophe Clavier, <a href="http://christophe.clavier.free.fr/Aliquot/site/database1/s0276.txt">Trajectory of 276 - the first 1576 terms and their factorizations</a>
%H A008892 Christophe Clavier, <a href="/A008892/a008892.txt">Trajectory of 276 - the first 1576 terms and their factorizations</a> [Cached copy]
%H A008892 Wolfgang Creyaufmüller, <a href="http://www.aliquot.de/lehmer.htm">Lehmer Five</a>
%H A008892 Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, <a href="http://math.dartmouth.edu/~carlp/iterate.pdf">On the normal behavior of the iterates of some arithmetic functions</a>, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.
%H A008892 Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, <a href="/A000010/a000010_1.pdf">On the normal behavior of the iterates of some arithmetic functions</a>, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]
%H A008892 FactorDB (factordb.com), <a href="http://factordb.com/sequences.php?se=1&amp;aq=276&amp;action=last20&amp;fr=0&amp;to=100">Search result for last 20 terms of 276 sequence</a>.
%H A008892 Brady Haran and Ben Sparks, <a href="https://www.youtube.com/watch?v=OtYKDzXwDEE">An amazing thing about 276</a>, Numberphile YouTube video, 2024.
%H A008892 N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, <a href="https://vimeo.com/237029685">Part I</a>, <a href="https://vimeo.com/237030304">Part 2</a>, <a href="https://oeis.org/A290447/a290447_slides.pdf">Slides.</a> (Mentions this sequence)
%H A008892 N. J. A. Sloane, <a href="https://arxiv.org/abs/2301.03149">"A Handbook of Integer Sequences" Fifty Years Later</a>, arXiv:2301.03149 [math.NT], 2023, p. 13.
%H A008892 Paul Zimmermann, <a href="http://www.loria.fr/~zimmerma/records/aliquot.html">Recent information</a>
%H A008892 <a href="/index/Al#ALIQUOT">Index entries for sequences related to aliquot parts</a>.
%F A008892 a(n+1) = A001065(a(n)). - _R. J. Mathar_, Oct 11 2017
%p A008892 f := proc(n) option remember; if n = 0 then 276; else sigma(f(n-1))-f(n-1); fi; end:
%t A008892 NestList[DivisorSigma[1, #] - # &, 276, 50] (* _Alonso del Arte_, Feb 24 2018 *)
%o A008892 (PARI) a(n, a=276)={for(i=1,n,a=sigma(a)-a);a} \\ _M. F. Hasler_, Feb 24 2018
%Y A008892 Cf. A001065, A098007 (length of aliquot sequences).
%Y A008892 Cf. A008885 (aliquot sequence starting at 30), ..., A008891 (starting at 180).
%K A008892 nonn
%O A008892 0,1
%A A008892 _N. J. A. Sloane_