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

2,2

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

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.

Example

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).

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]

Prog

(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

Crossrefs

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

Sequence in context: A272102 A056584 A135245 * A334657 A364241 A011514

Adjacent sequences: A135241 A135242 A135243 * A135245 A135246 A135247

Keyword

nonn

Author

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

Extensions

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

New name from Michel Marcus, Oct 31 2023

Status

approved