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A186273 a(n) is the least number k having exactly n representations as m + sigma(m), where sigma(m) is the sum of the divisors of m.

%I A186273 #19 Mar 13 2023 07:29:25
%S A186273 2,11,95,3623,2363,6143,21263,89303,202703,472973,493763,1013513,
%T A186273 3986483,3306713,2364863,21283763,19932413,29391863,74887313,98679263,
%U A186273 87499913,134797163,201013313,267843713,560472413,775337063,361823963,673985813
%N A186273 a(n) is the least number k having exactly n representations as m + sigma(m), where sigma(m) is the sum of the divisors of m.
%H A186273 Math Forum, <a href="http://mathforum.org/kb/message.jspa?messageID=7367658&amp;tstart=0">Topic: Petaflop machine not required / n + sigma(n)</a> [Broken link]
%e A186273 For the n-th term, the n solutions are
%e A186273 2     {1}
%e A186273 11    {4, 5}
%e A186273 95    {32, 39, 47}
%e A186273 3623  {1687, 1727, 1751, 1811}
%e A186273 2363  {1011, 1099, 1139, 1147, 1181}
%e A186273 6143  {2048, 2631, 2863, 2951, 2983, 3007}
%e A186273 21263 {9111, 10231, 10319, 10447, 10471, 10519, 10631}
%e A186273 89303 {38271, 41671, 42991, 43367, 44287, 44311, 44431, 44651}
%t A186273 nn=1000000; t=Table[n+DivisorSigma[1,n], {n, nn}]; t2=Select[t, # <= 2*nn+1&]; ts=Sort[Tally[t2]]; u=Union[Transpose[ts][[2]]]; c=Complement[Range[Max[u]], u]; If[c != {}, u=Range[c[[1]]-1]]; Table[Select[ts, #[[2]] == n &, 1][[1,1]], {n, u}]
%Y A186273 Cf. A007368 (smallest k such that sigma(x) = k has exactly n solutions).
%K A186273 nonn
%O A186273 1,1
%A A186273 _J. M. Bergot_, Feb 16 2011
%E A186273 Corrected and extended by _T. D. Noe_, Feb 16 2011
%E A186273 a(13)-a(28) from _Donovan Johnson_, Feb 17 2011