|
|
A008886
|
|
Aliquot sequence starting at 42.
|
|
4
|
|
|
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 aliquot parts A001065 are defined only for positive integers, so the trajectory ends when 0 is reached, here at index 14. - M. F. Hasler, Feb 24 2018
|
|
REFERENCES
|
R. K. Guy, Unsolved Problems in Number Theory, B6.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
f := proc(n) option remember; if n = 0 then 42; else sigma(f(n-1))-f(n-1); fi; end:
|
|
MATHEMATICA
|
Join[NestList[DivisorSigma[1, #]-#&, 42, 14], PadRight[{}, 60, 0]] (* Harvey P. Dale, Apr 28 2014 *)
|
|
PROG
|
(PARI) a(n, a=42)={for(i=1, n, a=sigma(a)-a); a} \\ M. F. Hasler, Feb 24 2018
|
|
CROSSREFS
|
Cf. A098007 (length of aliquot sequences); some other examples: A008885 (starting at 30) .. A008892 (starting at 276), A014360 (starting at 552) .. A014365 (starting at 1134), see link to index for a more complete list.
|
|
KEYWORD
|
nonn,fini,full
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|