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A008892
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Aliquot sequence starting at 276.
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25
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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
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0,1
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COMMENTS
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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.
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
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REFERENCES
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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.
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LINKS
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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)
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FORMULA
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MAPLE
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f := proc(n) option remember; if n = 0 then 276; else sigma(f(n-1))-f(n-1); fi; end:
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MATHEMATICA
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NestList[DivisorSigma[1, #] - # &, 276, 50] (* Alonso del Arte, Feb 24 2018 *)
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PROG
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(PARI) a(n, a=276)={for(i=1, n, a=sigma(a)-a); a} \\ M. F. Hasler, Feb 24 2018
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CROSSREFS
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Cf. A008885 (aliquot sequence starting at 30), ..., A008891 (starting at 180).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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