A008885 - OEIS

%I #31 Apr 25 2023 05:11:35

%S 30,42,54,66,78,90,144,259,45,33,15,9,4,3,1,0

%N Aliquot sequence starting at 30.

%C 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

%D Richard K. Guy, Unsolved Problems in Number Theory, B6.

%H Christophe CLAVIER, <a href="http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html">Aliquot Sequences</a>

%H R. J. Mathar, <a href="/A115350/a115350.pdf">Illustration of Aliquot Sequence Mergers</a> (2014) Fig 1 (prime family 3)

%H <a href="/index/Al#ALIQUOT">Index entries for sequences related to aliquot parts</a>.

%F a(n+1) = A001065(a(n)). - _R. J. Mathar_, Oct 11 2017

%e a(0) = 30.

%e 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.

%p f := proc(n) option remember; if n = 0 then 30; else sigma(f(n-1))-f(n-1); fi; end:

%t NestList[If[# > 0, DivisorSigma[1, #] - #, 0] &, 30, 80] (* _Harvey P. Dale_, Jun 12 2012 *)

%o (PARI) a(n, a=30)=for(i=1, n, a=sigma(a)-a); a \\ _M. F. Hasler_, Feb 24 2018

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

%K nonn,fini,full

%O 0,1

%A _N. J. A. Sloane_.

%E Edited by _M. F. Hasler_, Feb 24 2018