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A008892 Aliquot sequence starting at 276. 25
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. 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
The aliquot sequence starting at 306 joins this sequence after one step.
This sequence cannot be extended backwards, since A359132(276) = -1. - N. J. A. Sloane, Jan 10 2023
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
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].
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
Tyler Busby, Table of n, a(n) for n = 0..2146 (terms 0..2127 from Daniel Suteu, terms 2128..2140 from Jeppe Stig Nielsen)
Christophe Clavier, Aliquot Sequences
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]
Brady Haran and Ben Sparks, An amazing thing about 276, Numberphile YouTube video, 2024.
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)
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 13.
Paul Zimmermann, Recent information
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. A001065, 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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 20 18:00 EDT 2024. Contains 373532 sequences. (Running on oeis4.)