A048995 Numbers that are not the sum of the nontrivial factors (excluding 1 and n) of some natural number.

1, 4, 51, 87, 95, 119, 123, 145, 161, 187, 205, 209, 215, 237, 245, 247, 261, 267, 275, 287, 289, 291, 303, 305, 321, 323, 325, 335, 341, 371, 405, 407, 425, 429, 447, 471, 473, 497, 515, 517, 519, 529, 539, 551, 555, 561, 575, 583, 611, 623, 625, 627, 657

Offset: 1

Author

Bill Taylor (W.Taylor(AT)math.canterbury.ac.nz)

Keywords

• nonn
• nice

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)

Crossrefs

Complement of A048050.

Cf. A005114 (the same property with the sum of proper divisors) and A007369 (the same property with the sum of all divisors).

Programs

Mathematica

a048995[n_Integer] := Module[{t = Table[i, {i, n}], a048050, k},
  a048050[m_] := Plus @@ Take[Divisors[m], {2, -2}];
  Do[
   If[a048050[k] == 0 || a048050[k] > n, Null, t[[a048050[k]]] = 0],
   {k, 2, n^2}];
  Drop[DeleteDuplicates[t], {2}]
]; a048995[660] (* Michael De Vlieger, Nov 30 2014 *)

PARI

mx=8479; v=vector(mx); for(i=2, mx^2, ch=sigma(i)-i-1; if(ch<=mx, if(ch>0, v[ch]=1))); c=0; for(i=1, mx, if(v[i]==0, c++; write("b048995.txt", c " " i))) /* Donovan Johnson, Feb 11 2013 */

Extensions

Corrected and extended by Jud McCranie