A192270 Pseudo anti-perfect numbers.

5, 7, 8, 10, 17, 22, 23, 31, 32, 33, 35, 38, 39, 41, 45, 49, 52, 53, 56, 59, 60, 63, 67, 68, 70, 71, 72, 73, 74, 76, 77, 81, 82, 83, 85, 88, 94, 95, 98, 101, 102, 103, 104, 105, 108, 109, 110, 112, 115, 116, 117, 122, 123, 127, 129, 130, 137, 138, 143, 144, 147, 148, 149, 150, 151, 154, 157, 158, 162, 164, 165, 167, 171, 172, 175, 176, 178, 179, 182, 185

Offset

1,1

Comments

A pseudo anti-perfect number is a positive integer which is the sum of a subset of its anti-divisors. By definition, anti-perfect numbers (A073930) are a subset of this sequence.

Prime pseudo anti-perfect numbers begin: 5, 7, 17, 23, 31, 41, 53, 59, 67, 71, 73, 83, 101, 103, 109, 127, 137, 149, 151, 157, 167, 179, .... - Jonathan Vos Post, Jul 09 2011

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

39 is pseudo anti-perfect because its anti-divisors are 2, 6, 7, 11, 26 and the subset of 2, 11, and 26 adds up to 39.

Maple

with(combinat);
P:=proc(i)
local a, k, n, S;
for n from 1 to i do
  a:={};
  for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od;
  S:=subsets(a);
  while not S[finished] do
    if convert(S[nextvalue](), `+`)=n then print(n); break; fi;
  od;
od;
end:
P(10000);

Crossrefs

Cf. A005835, A066272, A192268.

Sequence in context: A059612 A314372 A314373 * A056657 A068312 A082097

Adjacent sequences: A192267 A192268 A192269 * A192271 A192272 A192273

Keyword

nonn

Author

Paolo P. Lava, Jun 28 2011

Status

approved