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A125601 a(n) is the smallest k > 0 such that there are exactly n numbers whose sum of proper divisors is k. 5
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A333445 A123930 A238895 * A292811 A025239 A127294
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Nov 27 2006
STATUS
approved

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Last modified September 22 10:53 EDT 2023. Contains 365520 sequences. (Running on oeis4.)