A008889 Aliquot sequence starting at 150.

150, 222, 234, 312, 528, 960, 2088, 3762, 5598, 6570, 10746, 13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754, 40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812, 2109796, 1889486, 953914, 668966, 353578, 176792

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Comments

Start at 150, and repeatedly apply the map x -> Sum of divisors of x excluding x.

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

• Ivan Panchenko, Table of n, a(n) for n = 0..177 (full sequence).
• Christophe CLAVIER, Aliquot Sequences
• Factordb, Whole sequence starting with 150
• 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 150; else sigma(f(n-1))-f(n-1); fi; end:

Mathematica

FixedPointList[If[# > 0, DivisorSigma[1, #] - #, 0]&, 150] // Most (* Jean-François Alcover, Mar 28 2020 *)

PARI

a(n,a=150)={for(i=1,n,a=sigma(a)-a);a} \\ M. F. Hasler, Feb 24 2018

Formula

a(n) = A008888(n+1). - R. J. Mathar, Oct 28 2008