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A192270 Pseudo anti-perfect numbers.

%I A192270 #16 Feb 04 2016 09:55:50
%S A192270 5,7,8,10,17,22,23,31,32,33,35,38,39,41,45,49,52,53,56,59,60,63,67,68,
%T A192270 70,71,72,73,74,76,77,81,82,83,85,88,94,95,98,101,102,103,104,105,108,
%U A192270 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
%N A192270 Pseudo anti-perfect numbers.
%C A192270 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.
%C A192270 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
%H A192270 Paolo P. Lava, <a href="/A192270/b192270.txt">Table of n, a(n) for n = 1..1000</a>
%e A192270 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.
%p A192270 with(combinat);
%p A192270 P:=proc(i)
%p A192270 local a,k,n,S;
%p A192270 for n from 1 to i do
%p A192270   a:={};
%p A192270   for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od;
%p A192270   S:=subsets(a);
%p A192270   while not S[finished] do
%p A192270     if convert(S[nextvalue](), `+`)=n then print(n); break; fi;
%p A192270   od;
%p A192270 od;
%p A192270 end:
%p A192270 P(10000);
%Y A192270 Cf. A005835, A066272, A192268.
%K A192270 nonn
%O A192270 1,1
%A A192270 _Paolo P. Lava_, Jun 28 2011