A186273 - OEIS

%I #19 Mar 13 2023 07:29:25

%S 2,11,95,3623,2363,6143,21263,89303,202703,472973,493763,1013513,

%T 3986483,3306713,2364863,21283763,19932413,29391863,74887313,98679263,

%U 87499913,134797163,201013313,267843713,560472413,775337063,361823963,673985813

%N 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 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 For the n-th term, the n solutions are

%e 2     {1}

%e 11    {4, 5}

%e 95    {32, 39, 47}

%e 3623  {1687, 1727, 1751, 1811}

%e 2363  {1011, 1099, 1139, 1147, 1181}

%e 6143  {2048, 2631, 2863, 2951, 2983, 3007}

%e 21263 {9111, 10231, 10319, 10447, 10471, 10519, 10631}

%e 89303 {38271, 41671, 42991, 43367, 44287, 44311, 44431, 44651}

%t 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 Cf. A007368 (smallest k such that sigma(x) = k has exactly n solutions).

%K nonn

%O 1,1

%A _J. M. Bergot_, Feb 16 2011

%E Corrected and extended by _T. D. Noe_, Feb 16 2011

%E a(13)-a(28) from _Donovan Johnson_, Feb 17 2011