

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
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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



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.


KEYWORD

nonn


AUTHOR



STATUS

approved



