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

1,1

Links

Table of n, a(n) for n=1..28.

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

Example

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}

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}]

Crossrefs

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

Sequence in context: A266834 A131407 A197994 * A349290 A332239 A261886

Adjacent sequences: A186270 A186271 A186272 * A186274 A186275 A186276

Keyword

nonn

Author

J. M. Bergot, Feb 16 2011

Extensions

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

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

Status

approved