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A008892 Aliquot sequence starting at 276. 21
276, 396, 696, 1104, 1872, 3770, 3790, 3050, 2716, 2772, 5964, 10164, 19628, 19684, 22876, 26404, 30044, 33796, 38780, 54628, 54684, 111300, 263676, 465668, 465724, 465780, 1026060, 2325540, 5335260, 11738916, 23117724, 45956820, 121129260, 266485716 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

It is an open question whether this sequence ever reaches 0. See A098007 and the Zimmermann link.

The aliquot sequence starting at 306 joins this sequence after one step.

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

REFERENCES

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

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.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..670

Christophe CLAVIER, Aliquot Sequences

Christophe CLAVIER, Trajectory of 276 - the first 1576 terms and their factorizations

Christophe CLAVIER, Trajectory of 276 - the first 1576 terms and their factorizations [Cached copy]

Wolfgang Creyaufmüller, Lehmer Five

Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.

Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]

N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

Paul Zimmermann, Latest information

Index entries for sequences related to aliquot parts.

FORMULA

a(n+1) = A001065(a(n)). - R. J. Mathar, Oct 11 2017

MAPLE

f := proc(n) option remember; if n = 0 then 276; else sigma(f(n-1))-f(n-1); fi; end:

MATHEMATICA

NestList[DivisorSigma[1, #] - # &, 276, 50] (* Alonso del Arte, Feb 24 2018 *)

PROG

(PARI) a(n, a=276)={for(i=1, n, a=sigma(a)-a); a} \\ M. F. Hasler, Feb 24 2018

CROSSREFS

Cf. A098007 (length of aliquot sequences).

Cf. A008885 (aliquot sequence starting at 30), ..., A008891 (starting at 180).

Sequence in context: A131884 A284279 A228517 * A216072 A284277 A133215

Adjacent sequences:  A008889 A008890 A008891 * A008893 A008894 A008895

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 20 19:36 EDT 2019. Contains 324234 sequences. (Running on oeis4.)