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

1,2

Links

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

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 *)

Prog

(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 */

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).

Sequence in context: A122464 A226375 A347551 * A215639 A320645 A347921

Adjacent sequences: A048992 A048993 A048994 * A048996 A048997 A048998

Keyword

nonn,nice

Author

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

Extensions

Corrected and extended by Jud McCranie

Status

approved