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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.

%I A125601 #37 Aug 09 2020 07:53:28
%S A125601 2,3,6,21,37,31,49,79,73,91,115,127,151,121,181,169,217,265,253,271,
%T A125601 211,301,433,379,331,361,457,391,451,655,463,541,421,775,511,769,673,
%U A125601 715,865,691,1015,631,1069,1075,721,931,781,1123,871,925,901,1177,991,1297
%N A125601 a(n) is the smallest k > 0 such that there are exactly n numbers whose sum of proper divisors is k.
%C A125601 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
%H A125601 Daniel Mondot, <a href="/A125601/b125601.txt">Table of n, a(n) for n = 0..5646</a> (First 157 terms from Ophir Spector. First 1000 terms from Ophir Spector and Donovan Johnson.)
%H A125601 W. Creyaufmueller, <a href="http://www.aliquot.de/aliquote.htm">Aliquot sequences</a>
%H A125601 Daniel Mondot, <a href="/A125601/a125601.txt">A-file, extended version of b-file but with some gaps towards the end.</a>
%H A125601 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Broken link]
%H A125601 J. O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Via Internet Archive Wayback-Machine]
%H A125601 J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a> [Cached copy, pdf file only]
%H A125601 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AliquotSequence.html">Aliquot sequence</a>
%e A125601 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.
%o A125601 (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],","))}
%Y A125601 Cf. A001065, A048138, A070015, A123930, A080907, A115350, A121507, A037020, A126016, A057709, A057710, A063990.
%K A125601 nonn
%O A125601 0,1
%A A125601 _Klaus Brockhaus_, Nov 27 2006