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

Author

Paolo P. Lava, Jun 28 2011

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A005835, A066272, A192268.

Programs

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);