A098007 -id:A098007 - cp's OEIS frontend

A008892 Aliquot sequence starting at 276.

276, 396, 696, 1104, 1872, 3770, 3790, 3050, 2716, 2772, 5964, 10164, 19628, 19684, 22876, 26404, 30044, 33796, 38780, 54628, 54684, 111300, 263676, 465668, 465724, 465780, 1026060, 2325540, 5335260, 11738916, 23117724, 45956820, 121129260, 266485716

Offset: 0

N. J. A. Sloane

nonn

It is an open question whether this sequence ever reaches 0. The trajectory has been calculated to 2145 terms, and is still growing, term 2145 being a 214-digit number (see FactorDB link). - N. J. A. Sloane, Jan 11 2023
The aliquot sequence starting at 306 joins this sequence after one step.
This sequence cannot be extended backwards, since A359132(276) = -1. - N. J. A. Sloane, Jan 10 2023
One can note that the k-tuple abundance of 276 is only 5, since a(6) = 3790 is deficient. On the other hand, the k-tuple abundance of a(8) = 2716 is 164 since a(172) is deficient (see A081705 for definition of k-tuple abundance). - Michel Marcus, Dec 31 2013

K. Chum, R. K. Guy, M. J. Jacobson, Jr., and A. S. Mosunov, Numerical and statistical analysis of aliquot sequences. Exper. Math. 29 (2020), no. 4, 414-425; arXiv:2110.14136, Oct. 2021 [math.NT].
Richard K. Guy, Unsolved Problems in Number Theory, B6.
Richard K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.

Tyler Busby, Table of n, a(n) for n = 0..2157 (terms 0..2127 from Daniel Suteu, terms 2128..2140 from Jeppe Stig Nielsen)
Christophe Clavier, Aliquot Sequences
Christophe Clavier, Trajectory of 276 - the first 1576 terms and their factorizations
Christophe Clavier, Trajectory of 276 - the first 1576 terms and their factorizations [Cached copy]
Wolfgang Creyaufmüller, Lehmer Five
Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.
Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]
FactorDB (factordb.com), Search result for last 20 terms of 276 sequence.
Brady Haran and Ben Sparks, An amazing thing about 276, Numberphile YouTube video, 2024.
N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 13.
Paul Zimmermann, Recent information
Index entries for sequences related to aliquot parts.

Cf. A001065, A098007 (length of aliquot sequences).

Cf. A008885 (aliquot sequence starting at 30), ..., A008891 (starting at 180).

f := proc(n) option remember; if n = 0 then 276; else sigma(f(n-1))-f(n-1); fi; end:

NestList[DivisorSigma[1, #] - # &, 276, 50] (* Alonso del Arte, Feb 24 2018 *)

a(n, a=276)={for(i=1,n,a=sigma(a)-a);a} \\ M. F. Hasler, Feb 24 2018

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

A098008 Length of transient part of aliquot sequence for n, or -1 if transient part is infinite.

Original entry on oeis.org

1, 2, 2, 3, 2, 0, 2, 3, 4, 4, 2, 7, 2, 5, 5, 6, 2, 4, 2, 7, 3, 6, 2, 5, 1, 7, 3, 0, 2, 15, 2, 3, 6, 8, 3, 4, 2, 7, 3, 4, 2, 14, 2, 5, 7, 8, 2, 6, 4, 3, 4, 9, 2, 13, 3, 5, 3, 4, 2, 11, 2, 9, 3, 4, 3, 12, 2, 5, 4, 6, 2, 9, 2, 5, 5, 5, 3, 11, 2, 7, 5, 6, 2, 6, 3, 9, 7, 7, 2, 10, 4, 6, 4, 4, 2, 9, 2, 3, 4, 5, 2, 18

Offset: 1

N. J. A. Sloane, Sep 09 2004

See A098007 for further information.
a(n) = 0 if and only if n is perfect (A000396) or part of a cycle of length greater than 1. - Comment corrected by Antti Karttunen, Nov 02 2017.
It is believed that the first time a(n) = -1 is at n = 276 (see A008892). - N. J. A. Sloane, Nov 02 2017

			From _Antti Karttunen_, Nov 02 2017: (Start)
For n = 3, a(n) = 2, because A001065(3) = 1 and A001065(1) = 0, so it took two steps to end in zero.
For n = 25, a(n) = 1, because A001065(25) = 6, and A001065(6) = 6, so it took one step to enter into a cycle.
For n = 12496, a(n) = 0, because 12496 is a member of 5-cycle of map n -> A001065(n) (see A072891).
(End)

R. K. Guy, Unsolved Problems in Number Theory, B6.
R. K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.

Antti Karttunen, Table of n, a(n) for n = 1..275

Cf. A001065, A098007, A044050, A003023, A008892. See A007906 for another version.

Cf. A206708 (gives a proper subset of zeros).

g[n_] := If[n > 0, DivisorSigma[1, n] - n, 0]; f[n_] := NestWhileList[g, n, UnsameQ, All]; Table[ Length[ f[n]] - 2, {n, 102}] (* good only for n<220 *) (* Robert G. Wilson v, Sep 10 2004 *)

(define (A098008 n) (let loop ((visited (list n)) (i 1)) (let ((next (A001065 (car visited)))) (cond ((zero? next) i) ((member next visited) => (lambda (transientplus1) (- (length transientplus1) 1))) (else (loop (cons next visited) (+ 1 i))))))) ;; Good for at least n = 1..275.
(define (A001065 n) (- (A000203 n) n)) ;; For an implementation of A000203, see under that entry.
;; Antti Karttunen, Nov 02 2017

More terms from Robert G. Wilson v, Sep 10 2004

A115350 Termination of the aliquot sequence starting at n.

Original entry on oeis.org

1, 2, 3, 3, 5, 6, 7, 7, 3, 7, 11, 3, 13, 7, 3, 3, 17, 11, 19, 7, 11, 7, 23, 17, 6, 3, 13, 28, 29, 3, 31, 31, 3, 7, 13, 17, 37, 7, 17, 43, 41, 3, 43, 43, 3, 3, 47, 41, 7, 43, 11, 3, 53, 3, 17, 41, 23, 31, 59, 43, 61, 7, 41, 41, 19, 3, 67, 31, 13, 43, 71, 3, 73, 43, 7, 41, 19, 3, 79, 41, 43, 43

Offset: 1

Sergio Pimentel, Mar 07 2006

nonn

Catalan's conjecture [not yet established and probably false] is that every aliquot sequence terminates in a prime number followed by 1, a perfect number, a friendly pair or an aliquot cycle.

a(n) = the prime number if the sequence terminates in a prime followed by 1, a(n) = a perfect number if the sequence terminates in a perfect number, a(n) = the smallest number of the cycle if the sequence terminates in an aliquot cycle, a(n) = 0 if the sequence is open ended. So far 276 is the smallest number for which the termination of the aliquot sequence is not known.

			a(12)=3 since the aliquot sequence starting at 12 is: 12 - 16 - 15 - 9 - 4 - 3.
a(95)=6 since the aliquot sequence starting at 95 is: 95 - 25 - 6 - 6 ...

W. Creyaufmueller, Aliquot Sequences.
R. J. Mathar, Table of n, a(n) for n= 1,...,12572 with -1 substituted for a(n) where terminations are not yet known.
R. J. Mathar, Illustration of Aliquot Sequence Mergers (2014)
Paul Zimmerman, Aliquot Sequences.

Cf. A098007, A098008, A098009, A098010, A003023, A044050, A007906, A037020, A063769, A005114.

a[n_] := If[n == 1, 1, FixedPointList[If[# > 0, DivisorSigma[1, #] - #, 0]&, n] /. {k__, 1, 0, 0} :> {k} // Last];
Array[a, 100] (* Jean-François Alcover, Mar 28 2020 *)

Edited by N. J. A. Sloane, Aug 14 2006

a(61)-a(80) from R. J. Mathar's list by Robert Price, Mar 16 2019

A098009 Numbers k such that the transient part of the aliquot sequence for k is finite and sets a new record.

Original entry on oeis.org

1, 2, 4, 9, 12, 30, 102, 138

Offset: 1

N. J. A. Sloane, Sep 10 2004

In order to extend this there is the problem that there are small numbers (276, 552, etc.) for which it is not presently known if they cycle. I propose that we assume these do not cycle, but mark the records beyond where this becomes an issue as conjectural only.

			138 has a transient of length 177 (see Guy's book).

See references and links in A098007, A098008.

Records in A098008. Cf. A098010.

g[n_] := If[n > 0, DivisorSigma[1, n] - n, 0]; f[n_] := NestWhileList[g, n, UnsameQ, All]; a = -1; Do[b = Length[ f[n]] - 1; If[b > a, a = b; Print[n]], {n, 275}] (* Robert G. Wilson v, Sep 10 2004 *)

102 and 138 from Robert G. Wilson v, Sep 10 2004

A127661 Lengths of the infinitary aliquot sequences.

Original entry on oeis.org

2, 3, 3, 3, 3, 1, 3, 4, 3, 5, 3, 5, 3, 6, 4, 3, 3, 6, 3, 6, 4, 7, 3, 8, 3, 4, 4, 6, 3, 6, 3, 4, 5, 7, 4, 7, 3, 8, 4, 8, 3, 5, 3, 4, 5, 5, 3, 7, 3, 7, 5, 7, 3, 4, 4, 6, 4, 5, 3, 1, 3, 8, 4, 5, 4, 3, 3, 8, 5, 10, 3, 3, 3, 9, 4, 9, 4, 2, 3, 8, 3, 5, 3, 10, 4, 6, 6, 8, 3, 1, 5, 7, 5, 8, 4, 9, 3, 8, 5, 7

Offset: 1

Ant King, Jan 26 2007

nonn

An infinitary aliquot sequence is defined by the map x->A049417(x)-x. The map usually terminates with a zero, but may enter cycles (if n in A127662 for example).
The length of an infinitary aliquot sequence is defined to be the length of its transient part + the length of its terminal cycle.
The value of a(840) starting the infinitary aliquot sequence 840 -> 2040 -> 4440 -> 9240 -> 25320,... is >1500. - R. J. Mathar, Oct 05 2017

			a(4)=3 because the infinitary aliquot sequence generated by 4 is 4 -> 1 -> 0 and it has length 3.
a(6) = 1 because 6 -> 6 -> 6 ->... enters a cycle after 1 term.
a(8) = 4 because 8 -> 7 -> 1 -> 0 terminates after 4 terms.
a(30) = 6 because 30 ->42 -> 54 -> 66 -> 78 -> 90 -> 90 -> 90 -> ...enters a cycle after 6 terms.
a(126)=2 because 126 -> 114 -> 126 enters a cycle after 2 terms.

R. J. Mathar, Table of n, a(n) for n = 1..839
Graeme L. Cohen, On an integer's infinitary divisors, Math. Comp., 54 (1990), 395-411.
Hans Havermann, Graphs of infinitary aliquot sequences for 840, 1152, 2442, 2658, 2982, 5766, 6216, 6870, 7560, 8670, 9030, 9570 (click to see full plots)
D. Moews, A database of aliquot cycles (2015)
J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]
J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]
J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]

Cf. A126168, A127662 - A127667, A293355, A098007.

# Uses code snippets of A049417
A127661 := proc(n)
    local trac,x;
    x := n ;
    trac := [x] ;
    while true do
        x := A049417(x)-trac[-1] ;
        if x = 0 then
            return 1+nops(trac) ;
        elif x in trac then
            return nops(trac) ;
        end if;
        trac := [op(trac),x] ;
    end do:
end proc:
seq(A127661(n),n=1..100) ; # R. J. Mathar, Oct 05 2017

ExponentList[n_Integer,factors_List]:={#,IntegerExponent[n,# ]}&/@factors;InfinitaryDivisors[1]:={1}; InfinitaryDivisors[n_Integer?Positive]:=Module[ { factors=First/@FactorInteger[n], d=Divisors[n] }, d[[Flatten[Position[ Transpose[ Thread[Function[{f,g}, BitOr[f,g]==g][ #,Last[ # ]]]&/@ Transpose[Last/@ExponentList[ #,factors]&/@d]],?(And@@#&),{1}]] ]] ]; properinfinitarydivisorsum[k]:=Plus@@InfinitaryDivisors[k]-k;g[n_] := If[n > 0,properinfinitarydivisorsum[n], 0];iTrajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]];Length[iTrajectory[ # ]] &/@ Range[100]
(* Second program: *)
A049417[n_] := If[n == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]] // Total;
A127661[n_] := Module[{trac, x}, x = n; trac = {x}; While[True, x = A049417[x] - trac[[-1]]; If[x == 0, Return[1 + Length[trac]], If[MemberQ[trac, x], Return[Length[trac]]]]; trac = Append[trac, x]]];
Table[A127661[n], {n, 1, 100}] (* Jean-François Alcover, Aug 28 2023, after R. J. Mathar *)

A003023 "Length" of aliquot sequence for n.

Original entry on oeis.org

0, 1, 1, 2, 1, 1, 1, 2, 3, 3, 1, 6, 1, 4, 4, 5, 1, 3, 1, 6, 2, 5, 1, 4, 2, 6, 2, 1, 1, 14, 1, 2, 5, 7, 2, 3, 1, 6, 2, 3, 1, 13, 1, 4, 6, 7, 1, 5, 3, 2, 3, 8, 1, 12, 2, 4, 2, 3, 1, 10, 1, 8, 2, 3, 2, 11, 1, 4, 3, 5, 1, 8, 1, 4, 4, 4, 2, 10, 1, 6, 4, 5, 1, 5, 2, 8, 6, 6, 1, 9, 3, 5, 3, 3, 3, 8, 1, 2, 3, 4, 1, 17

Offset: 1

N. J. A. Sloane

The aliquot sequence for n is the trajectory of n under repeated application of the map x -> sigma(x) - x.
The trajectory will either have a transient part followed by a cyclic part, or will have an infinite transient part and never cycle.
Sequence gives (length of transient part of trajectory) - 1 (if trajectory ends at 1), or provided that it ends in cycle [e.g., (6) or (220 284)], gives (length of transient part of trajectory) + (length of cycle) = length of trajectory. - Corrected by Antti Karttunen, Nov 03 2017
See A098007 for a better version.
The function sigma = A000203 is defined only on the positive integers and not for 0, so the trajectory ends when 0 is reached. - M. F. Hasler, Nov 16 2013

			Examples of trajectories:
1, 0, 0, ...
2, 1, 0, 0, ...
3, 1, 0, 0, ... (and similarly for any prime)
4, 3, 1, 0, 0, ...
5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
6, 6, 6, ... (and similarly for any perfect number)
8, 7, 1, 0, 0, ...
9, 4, 3, 1, 0, 0, ...
12, 16, 15, 9, 4, 3, 1, 0, 0, ...
14, 10, 8, 7, 1, 0, 0, ...
25, 6, 6, 6, ...
28, 28, 28, ... (the next perfect number)
30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0, 0, ...
42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0, 0, ...

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
R. K. Guy, Unsolved Problems in Number Theory, B6.
R. K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Antti Karttunen, Table of n, a(n) for n = 1..275 (fate of 276 is unknown)
R. K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971. [Annotated scanned copy]
F. Richman, Aliquot series: Abundant, deficient, perfect
Eric Weisstein's World of Mathematics, Aliquot Sequence
Wikipedia, Aliquot sequence

Cf. A001065, A098007.

Cf. A059447 (least k such that n is the length of the aliquot sequence for k ending at 1).

f:=proc(n) local t1, i,j,k; t1:=[n]; for i from 2 to 50 do j:= t1[i-1]; k:=sigma(j)-j; t1:=[op(t1), k]; od: t1; end; # produces trajectory for n

f[x_] := (k++; DivisorSigma[1, x] - x); f[1] = 1;
Table[k = 0; FixedPoint[f, n]; k, {n, 1, 102}]
(* Jean-François Alcover, Jul 27 2011 *)

s := func(_plus(op(numlib::divisors(n)))-n,n): A003023 := proc(n) local i,T,m; begin m := n; i := 1; while T[ m ]<>1 and m<>1 do T[ m ] := 1; m := s(m); i := i+1 end_while; i-1 end_proc:

(define (A003023 n) (let loop ((visited (list n)) (i 0)) (let ((next (A001065 (car visited)))) (cond ((zero? next) i) ((member next visited) (+ 1 i)) (else (loop (cons next visited) (+ 1 i)))))))
(define (A001065 n) (- (A000203 n) n)) ;; For an implementation of A000203, see under that entry.
;; Antti Karttunen, Nov 03 2017

More terms from Matthew Conroy, Jan 16 2006

A007906 Number of steps for aliquot sequence for n to converge to 0, or -1 if it never reaches 0.

Original entry on oeis.org

1, 2, 2, 3, 2, -1, 2, 3, 4, 4, 2, 7, 2, 5, 5, 6, 2, 4, 2, 7, 3, 6, 2, 5, -1, 7, 3, -1, 2, 15, 2, 3, 6, 8, 3, 4, 2, 7, 3, 4, 2, 14, 2, 5, 7, 8, 2, 6, 4, 3, 4, 9, 2, 13, 3, 5, 3, 4, 2, 11, 2, 9, 3, 4, 3, 12, 2, 5, 4, 6, 2, 9, 2, 5, 5, 5, 3, 11, 2, 7, 5, 6, 2, 6, 3, 9, 7, 7, 2, 10, 4, 6, 4, 4, -1, 9, 2, 3

Offset: 1

Michael Gerenrot (sch116(AT)yahoo.com)

sign

Length of transient part of trajectory of n if trajectory reaches 1, otherwise a(n) = -1. See A098008 for another version. See A098007 for further information.

R. K. Guy, Unsolved Problems in Number Theory, B6.
R. K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.

Antti Karttunen, Table of n, a(n) for n = 1..275

Cf. A098008, A098007, A044050, A003023.

(define (A007906 n) (let loop ((visited (list n)) (i 1)) (let ((next (A001065 (car visited)))) (cond ((zero? next) i) ((member next visited) -1) (else (loop (cons next visited) (+ 1 i)))))))
(define (A001065 n) (- (A000203 n) n)) ;; For an implementation of A000203, see under that entry.
;; Antti Karttunen, Nov 02 2017

Definition changed by N. J. A. Sloane, Nov 02 2017 at the suggestion of Antti Karttunen.

A008888 Aliquot sequence starting at 138.

Original entry on oeis.org

138, 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

N. J. A. Sloane

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 178. - M. F. Hasler, Feb 24 2018

Merges into sequence A008889 after the first step.

R. K. Guy, Unsolved Problems in Number Theory, B6.
Enoch Haga, Exploring Prime Numbers on Your PC, 2nd ed., 1998, pages 83-84 and Table 8, page 46. ISBN 1-885794-16-9.

T. D. Noe, Table of n, a(n) for n = 0..178 (full sequence).
Christophe Clavier, Aliquot Sequences
Passawan Noppakaew and Prapanpong Pongsriiam, Product of Some Polynomials and Arithmetic Functions, J. Int. Seq. (2023) Vol. 26, Art. 23.9.1.
Index entries for sequences related to aliquot parts.

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

f := proc(n) option remember; if n = 0 then 138; else sigma(f(n-1))-f(n-1); fi; end:

FixedPointList[If[# > 0, DivisorSigma[1, #] - #, 0]&, 138] // Most (* Jean-François Alcover, Mar 28 2020 *)

a(n,a=138)={for(i=1,n,a=sigma(a)-a);a} \\ M. F. Hasler, Feb 24 2018

a(n) = A001065(a(n-1)) for n > 0, thus a(n) = A001065^n(138) for all n < 179. - M. F. Hasler, Nov 16 2013

a(n) = A008889(n-1) for all n >= 1. - M. F. Hasler, Feb 24 2018

Term 179 removed from b-file by Ivan Panchenko, Nov 16 2013

Edited by M. F. Hasler, Feb 24 2018

A014360 Aliquot sequence starting at 552.

Original entry on oeis.org

552, 888, 1392, 2328, 3552, 6024, 9096, 13704, 20616, 30984, 46536, 86904, 165816, 367704, 628356, 837836, 628384, 630356, 491884, 368920, 499400, 772840, 978650, 975652, 744248, 696712, 628628, 857836, 857892, 1472268

Offset: 0

Paul Zimmermann

nonn

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

Tyler Busby, Table of n, a(n) for n = 0..1181 (terms 0..352 from T. D. Noe)
Christophe Clavier, Aliquot Sequences
Paul Zimmermann, Latest information
Index entries for sequences related to aliquot parts.

Cf. A001065, A098007 (length of aliquot sequences).

Some other examples: A008885 (starting at 30) .. A008892 (starting at 276), A014361 (starting at 564) .. A014365 (starting at 1134), see link to index for a more complete list.

FixedPointList[If[# > 0, DivisorSigma[1, #] - #, 0]&, 552, 100] (* Jean-François Alcover, Mar 28 2020 *)

a(n, a=552)={for(i=1, n, a=sigma(a)-a); a} \\ M. F. Hasler, Feb 24 2018

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

A014365 Aliquot sequence starting at 1134.

Original entry on oeis.org

1134, 1770, 2550, 4146, 4158, 7362, 8628, 11532, 16272, 29670, 46362, 46374, 48666, 48678, 70362, 86118, 92058, 95622, 95634, 180846, 246834, 381006, 460458, 562902, 612138, 612150, 1316298, 1350582, 1509690, 3086790

Offset: 0

Paul Zimmermann

nonn

Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B6, pp. 92-95.

Amiram Eldar, Table of n, a(n) for n = 0..3839 (terms 0..3568 from Robert G. Wilson v)
Christophe Clavier, Aliquot Sequences.
factordb.com, Aliquot sequence of 1134.
Robert G. Wilson v, terms n = 0..3568 with factorization.
Paul Zimmermann, Latest information.
Index entries for sequences related to aliquot parts.

Cf. A098007 (length of aliquot sequences); some other examples: A008885 (starting at 30) .. A008892 (starting at 276), A014360 (starting at 552) .. A014364 (starting at 1074), see link to index for a more complete list.

Cf. A001065.

f[n_] := DivisorSigma[1, n] - n; NestList[f, 1134, 100] (* Robert G. Wilson v, Dec 22 2012 *)

a(n, a=1134)={for(i=1, n, a=sigma(a)-a); a} \\ M. F. Hasler, Feb 25 2018

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

cp's OEIS Frontend

A008892 Aliquot sequence starting at 276.

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A098008 Length of transient part of aliquot sequence for n, or -1 if transient part is infinite.

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A115350 Termination of the aliquot sequence starting at n.

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A098009 Numbers k such that the transient part of the aliquot sequence for k is finite and sets a new record.

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A127661 Lengths of the infinitary aliquot sequences.

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A003023 "Length" of aliquot sequence for n.

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A007906 Number of steps for aliquot sequence for n to converge to 0, or -1 if it never reaches 0.

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