cp's OEIS Frontend

A135244 Largest m such that the sum of the aliquot parts of m (A001065) equals n, or 0 if no such number exists.

%I A135244 #34 Feb 16 2025 08:33:07
%S A135244 0,4,9,0,25,8,49,15,14,21,121,35,169,33,26,55,289,77,361,91,38,85,529,
%T A135244 143,46,133,28,187,841,221,961,247,62,253,24,323,1369,217,81,391,1681,
%U A135244 437,1849,403,86,493,2209,551,94,589,0,667,2809,713,106,703,68,697,3481
%N A135244 Largest m such that the sum of the aliquot parts of m (A001065) equals n, or 0 if no such number exists.
%C A135244 Previous name: Aliquot predecessors with the largest values.
%C A135244 Find each node's predecessors in aliquot sequences and choose the largest predecessor.
%C A135244 Climb the aliquot trees on shortest paths (see A135245 = Climb the aliquot trees on thickest branches).
%C A135244 The sequence starts at offset 2, since all primes satisfy sigma(n)-n = 1. - _Michel Marcus_, Nov 11 2014
%H A135244 Amiram Eldar, <a href="/A135244/b135244.txt">Table of n, a(n) for n = 2..10000</a> (terms 2..150 from Ophir Spector)
%H A135244 Wolfgang Creyaufmueller, <a href="http://www.aliquot.de/aliquote.htm">Aliquot sequences</a>.
%H A135244 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a>. [Broken link]
%H A135244 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 A135244 J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a>. [Cached copy, pdf file only]
%H A135244 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AliquotSequence.html">Aliquot sequence</a>.
%e A135244 a(25) = 143 since 25 has 3 predecessors (95,119,143), 143 being the largest.
%e A135244 a(5) = 0 since it has no predecessors (see Untouchables - A005114).
%t A135244 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 A135244 (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 A135244 Cf. A001065, A005114, A125601, A135245, A057709, A057710, A063769, A080907, A121507, A037020, A126016.
%K A135244 nonn
%O A135244 2,2
%A A135244 Ophir Spector (ospectoro(AT)yahoo.com), Nov 25 2007
%E A135244 a(1)=0 removed and offset set to 2 by _Michel Marcus_, Nov 11 2014
%E A135244 New name from _Michel Marcus_, Oct 31 2023