A008886 Aliquot sequence starting at 42.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

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

• Christophe CLAVIER, Aliquot Sequences
• Index entries for sequences related to aliquot parts.

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.

Programs

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 *)

PARI

a(n,a=42)={for(i=1,n,a=sigma(a)-a);a} \\ M. F. Hasler, Feb 24 2018

Formula

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

a(n) = A008885(n+1). - R. J. Mathar, Jan 12 2024

Extensions

Edited by M. F. Hasler, Feb 24 2018