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.

2, 11, 95, 3623, 2363, 6143, 21263, 89303, 202703, 472973, 493763, 1013513, 3986483, 3306713, 2364863, 21283763, 19932413, 29391863, 74887313, 98679263, 87499913, 134797163, 201013313, 267843713, 560472413, 775337063, 361823963, 673985813

Offset: 1

Author

J. M. Bergot, Feb 16 2011

Keywords

• nonn

Examples

			For the n-th term, the n solutions are
2     {1}
11    {4, 5}
95    {32, 39, 47}
3623  {1687, 1727, 1751, 1811}
2363  {1011, 1099, 1139, 1147, 1181}
6143  {2048, 2631, 2863, 2951, 2983, 3007}
21263 {9111, 10231, 10319, 10447, 10471, 10519, 10631}
89303 {38271, 41671, 42991, 43367, 44287, 44311, 44431, 44651}
		

Links

• Math Forum, Topic: Petaflop machine not required / n + sigma(n) [Broken link]

Crossrefs

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

Programs

Mathematica

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}]

Extensions

Corrected and extended by T. D. Noe, Feb 16 2011

a(13)-a(28) from Donovan Johnson, Feb 17 2011