

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
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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 214digit 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 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

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, 414425; 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. 557580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.


LINKS

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)


FORMULA



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


KEYWORD

nonn


AUTHOR



STATUS

approved



