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

0, 4, 9, 0, 25, 8, 49, 15, 14, 21, 121, 35, 169, 33, 26, 55, 289, 77, 361, 91, 38, 85, 529, 143, 46, 133, 28, 187, 841, 221, 961, 247, 62, 253, 24, 323, 1369, 217, 81, 391, 1681, 437, 1849, 403, 86, 493, 2209, 551, 94, 589, 0, 667, 2809, 713, 106, 703, 68, 697, 3481

Offset: 2

Author

Ophir Spector (ospectoro(AT)yahoo.com), Nov 25 2007

Keywords

• nonn

Comments

Previous name: Aliquot predecessors with the largest values.

Find each node's predecessors in aliquot sequences and choose the largest predecessor.

Climb the aliquot trees on shortest paths (see A135245 = Climb the aliquot trees on thickest branches).

The sequence starts at offset 2, since all primes satisfy sigma(n)-n = 1. - Michel Marcus, Nov 11 2014

Examples

			a(25) = 143 since 25 has 3 predecessors (95,119,143), 143 being the largest.
a(5) = 0 since it has no predecessors (see Untouchables - A005114).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10000 (terms 2..150 from Ophir Spector)
• Wolfgang Creyaufmueller, Aliquot sequences.
• 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]
• Eric Weisstein's World of Mathematics, Aliquot sequence.

Crossrefs

Cf. A001065, A005114, A125601, A135245, A057709, A057710, A063769, A080907, A121507, A037020, A126016.

Programs

Mathematica

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]

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

Extensions

a(1)=0 removed and offset set to 2 by Michel Marcus, Nov 11 2014

New name from Michel Marcus, Oct 31 2023