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A192270 Pseudo anti-perfect numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A288735 A080707 A059612 * A056657 A068312 A082097

Adjacent sequences:  A192267 A192268 A192269 * A192271 A192272 A192273

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Jun 28 2011

STATUS

approved

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Last modified August 21 00:45 EDT 2017. Contains 290855 sequences.