

A008885


Aliquot sequence starting at 30.


15



30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0
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OFFSET

0,1


COMMENTS

The sumofdivisor function A000203 and thus aliquot parts A001065 are defined only for positive integers, so the trajectory ends when 0 is reached, here at index 15.  M. F. Hasler, Feb 24 2018


REFERENCES

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


LINKS

Table of n, a(n) for n=0..15.
Christophe CLAVIER, Aliquot Sequences
Index entries for sequences related to aliquot parts.


FORMULA

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


EXAMPLE

a(0) = 30.
30 has eight divisors, 1, 2, 3, 5, 6, 10, 15, 30, which add up to 72, and 72  30 = 42, so a(1) = 42.


MAPLE

f := proc(n) option remember; if n = 0 then 30; else sigma(f(n1))f(n1); fi; end:


MATHEMATICA

NestList[If[# > 0, DivisorSigma[1, #]  #, 0] &, 30, 80] (* Harvey P. Dale, Jun 12 2012 *)


PROG

(PARI) a(n, a=30)=for(i=1, n, a=sigma(a)a); a \\ M. F. Hasler, Feb 24 2018


CROSSREFS

Cf. A008886, A0088867, A008888, A008889, A008890, A008891, A008892.
Sequence in context: A110849 A074696 A127663 * A097036 A090790 A090800
Adjacent sequences: A008882 A008883 A008884 * A008886 A008887 A008888


KEYWORD

nonn,fini,full


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Edited by M. F. Hasler, Feb 24 2018


STATUS

approved



