A125601 a(n) is the smallest k > 0 such that there are exactly n numbers whose sum of proper divisors is k.

2, 3, 6, 21, 37, 31, 49, 79, 73, 91, 115, 127, 151, 121, 181, 169, 217, 265, 253, 271, 211, 301, 433, 379, 331, 361, 457, 391, 451, 655, 463, 541, 421, 775, 511, 769, 673, 715, 865, 691, 1015, 631, 1069, 1075, 721, 931, 781, 1123, 871, 925, 901, 1177, 991, 1297

Offset

0,1

Comments

Minimal values for nodes of exact degree in aliquot sequences. Find each node's degree (number of predecessors) in aliquot sequences and choose the smallest value as the sequence member. - Ophir Spector, ospectoro (AT) yahoo.com Nov 25 2007

Links

Daniel Mondot, Table of n, a(n) for n = 0..5646 (First 157 terms from Ophir Spector. First 1000 terms from Ophir Spector and Donovan Johnson.)

W. Creyaufmueller, Aliquot sequences

Daniel Mondot, A-file, extended version of b-file but with some gaps towards the end.

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(4) = 37 since there are exactly four numbers (155, 203, 299, 323) whose sum of proper divisors is 37. For k < 37 there are either fewer or more numbers (32, 125, 161, 209, 221 for k = 31) whose sum of proper divisors is k.

Prog

(PARI) {m=54; z=1500; y=600000; v=vector(z); for(n=2, y, s=sigma(n)-n; if(s<z, v[s]++)); w=vector(m, i, -1); for(j=2, z, if(v[j]<m&&w[v[j]+1]<0, w[v[j]+1]=j)); for(j=1, m, print1(w[j], ", "))}

Crossrefs

Cf. A001065, A048138, A070015, A123930, A080907, A115350, A121507, A037020, A126016, A057709, A057710, A063990.

Sequence in context: A333445 A123930 A238895 * A292811 A025239 A127294

Adjacent sequences: A125598 A125599 A125600 * A125602 A125603 A125604

Keyword

nonn

Author

Klaus Brockhaus, Nov 27 2006

Status

approved