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A008885 Aliquot sequence starting at 30. 15
30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The sum-of-divisor 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(n-1))-f(n-1); 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 - 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

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)