

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
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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 ktuple abundance of 276 is only 5, since a(6) = 3790 is deficient. On the other hand, the ktuple abundance of a(8) = 2716 is 164 since a(172) is deficient (see A081705 for definition of ktuple 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. 557580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.


LINKS

Daniel Suteu, Table of n, a(n) for n = 0..2127 (first 671 terms from T. D. Noe)
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. 165204.
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. 165204. [Annotated copy with Anumbers]
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(n1))f(n1); 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



