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%I #33 Oct 31 2023 08:29:36
%S 0,4,9,0,25,8,49,15,14,21,121,35,169,33,26,55,289,77,361,91,38,85,529,
%T 143,46,133,28,187,841,221,961,247,62,253,24,323,1369,217,81,391,1681,
%U 437,1849,403,86,493,2209,551,94,589,0,667,2809,713,106,703,68,697,3481
%N Largest m such that the sum of the aliquot parts of m (A001065) equals n, or 0 if no such number exists.
%C Previous name: Aliquot predecessors with the largest values.
%C Find each node's predecessors in aliquot sequences and choose the largest predecessor.
%C Climb the aliquot trees on shortest paths (see A135245 = Climb the aliquot trees on thickest branches).
%C The sequence starts at offset 2, since all primes satisfy sigma(n)-n = 1. - _Michel Marcus_, Nov 11 2014
%H Amiram Eldar, <a href="/A135244/b135244.txt">Table of n, a(n) for n = 2..10000</a> (terms 2..150 from Ophir Spector)
%H Wolfgang Creyaufmueller, <a href="http://www.aliquot.de/aliquote.htm">Aliquot sequences</a>.
%H J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a>. [Broken link]
%H J. O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a>. [Via Internet Archive Wayback-Machine]
%H J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a>. [Cached copy, pdf file only]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AliquotSequence.html">Aliquot sequence</a>.
%e a(25) = 143 since 25 has 3 predecessors (95,119,143), 143 being the largest.
%e a(5) = 0 since it has no predecessors (see Untouchables - A005114).
%t seq[max_] := Module[{s = Table[0, {n, 1, max}], i}, Do[If[(i = DivisorSigma[1, n] - n) <= max, s[[i]] = Max[s[[i]], n]], {n, 2, (max - 1)^2}]; Rest @ s]; seq[50]
%o (PARI) lista(nn) = {for (n=2, nn, k = (n-1)^2; while(k && (sigma(k)-k != n), k--); print1(k, ", "););} \\ _Michel Marcus_, Nov 11 2014
%Y Cf. A001065, A005114, A125601, A135245, A057709, A057710, A063769, A080907, A121507, A037020, A126016.
%K nonn
%O 2,2
%A Ophir Spector (ospectoro(AT)yahoo.com), Nov 25 2007
%E a(1)=0 removed and offset set to 2 by _Michel Marcus_, Nov 11 2014
%E New name from _Michel Marcus_, Oct 31 2023