A008891 Aliquot sequence starting at 180.

180, 366, 378, 582, 594, 846, 1026, 1374, 1386, 2358, 2790, 4698, 6192, 11540, 12736, 12664, 11096, 11104, 10820, 11944, 10466, 5236, 6860, 9940, 14252, 14308, 15218, 10894, 6746, 3376, 3196, 2852, 2524, 1900, 2440, 3140, 3496, 3704, 3256, 3584, 4600, 6560, 9316, 8072, 7078, 3542, 3370, 2714, 1606, 1058, 601, 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 52. - M. F. Hasler, Feb 24 2018

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 0..52
• Christophe CLAVIER, Aliquot Sequences
• Index entries for sequences related to aliquot parts.

Crossrefs

Cf. A008885 (starting at 30), ..., A008892 (starting at 276), A098007 (length of aliquot sequences).

Programs

Maple

f := proc(n) option remember; if n = 0 then 180; else sigma(f(n-1))-f(n-1); fi; end:

Mathematica

FixedPointList[If[# > 0, DivisorSigma[1, #] - #, 0]&, 180] // Most (* Jean-François Alcover, Mar 28 2020 *)

PARI

a(n,a=180)={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