A192285 Primitive pseudo anti-perfect numbers.

5, 7, 8, 17, 22, 23, 31, 33, 38, 39, 41, 52, 53, 59, 67, 71, 73, 74, 81, 83, 94, 101, 103, 108, 109, 116, 122, 127, 129, 137, 143, 149, 151, 157, 158, 167, 171, 172, 178, 179, 193, 199, 214, 237, 241, 247, 257, 262, 263, 269, 283, 293, 311, 313, 319, 331, 333

Offset: 1

Author

Paolo P. Lava, Jul 20 2011

Keywords

• nonn

Comments

A primitive pseudo anti-perfect number is a pseudo anti-perfect number that is not a multiple of any other pseudo anti-perfect number.

Like A006036 but using anti-divisors.

Subset of A192270.

Crossrefs

Cf. A006036, A066272, A192270

Programs

Maple

with(combinat);
P:=proc(i)
local a,j,k,n,ok,S,v;
v:=array(1..10000); j:=0;
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
       if j=0 then j:=1; v[1]:=n; print(n); break;
       else
          ok:=1;
          for k from 1 to j do
              if trunc(n/v[k])=n/v[k] then ok:=0; break; fi;
          od;
          j:=j+1; v[j]:=n; if ok=1 then print(n); fi;
       fi;
    fi;
  od;
od;
end: