A008885 Aliquot sequence starting at 30.

30, 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 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

Examples

			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.
		

References

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

Links

• Christophe CLAVIER, Aliquot Sequences
• R. J. Mathar, Illustration of Aliquot Sequence Mergers (2014) Fig 1 (prime family 3)
• Index entries for sequences related to aliquot parts.

Crossrefs

Cf. A008886, A008887, A008888, A008889, A008890, A008891, A008892.

Programs

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 *)

PARI

a(n, a=30)=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

Extensions

Edited by M. F. Hasler, Feb 24 2018