A192270 -id:A192270 - cp's OEIS frontend

A192271 Anti-weird numbers.

11, 12, 13, 14, 15, 18, 20, 21, 25, 27, 28, 30, 37, 40, 42, 43, 46, 47, 48, 50, 55, 57, 58, 62, 65, 66, 75, 78, 80, 84, 86, 87, 90, 91, 92, 93, 97, 99, 100, 107, 111, 113, 118, 119, 120, 121, 124, 125, 126, 128, 132, 133, 135, 136, 140, 142, 145, 152, 153, 155, 160, 161, 163, 168, 170, 173, 177, 180, 181, 183, 184, 186, 188, 190, 192, 196, 197, 198, 204, 205, 208, 210, 212, 213, 218, 222, 223

Offset: 1

Paolo P. Lava, Jun 28 2011

nonn

Like A006037 but using anti-divisors: Anti-weird numbers are anti-abundant (A192268) but not pseudo anti-perfect (A192270).

			25 is an anti-weird number because it is anti-abundant (its anti-divisors are 2, 3, 7, 10, 17 and their sum is 39 > 25) and no subsets of its anti-divisors add up to 25.

Cf. A006037, A066272, A192268, A192270.

# see A066272
isA192270 := proc(n) local a,S ; a := antidivisors(n) ;  S := combinat[subsets](a) ; while not S[finished] do if convert(S[nextvalue](),`+`) = n then return true; end if; end do; false ; end proc:
isA192268 := proc(n) A066417(n) > n ; end proc:
isA192271 := proc(n) isA192268(n) and not isA192270(n) ; end proc:
for n from 1 to 40 do if isA192271(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Jul 04 2011

A192285 Primitive pseudo anti-perfect numbers.

Original entry on oeis.org

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

Paolo P. Lava, Jul 20 2011

nonn

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.

Cf. A006036, A066272, A192270

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:

A240968 Unitary anti-perfect numbers.

Original entry on oeis.org

5, 8, 10, 41, 206, 1066, 2412, 3281, 8086, 11570, 29525, 57012, 73728, 410390, 413486, 775130, 2391485, 2454146, 2937446, 64563520, 100531166, 152032126, 988747406

Offset: 1

Paolo P. Lava, Aug 05 2014

For any number x we consider the sum of its anti-divisors which are coprime to x (unitary anti-divisors). The sequence list the numbers for which this sum is equal to x.
Subset of A192270.
I found only 2 unitary anti-amicable numbers: 18208, 20470.
No other terms < 2147000000. Jud McCranie, Sep 21 2019.

			Anti-divisors of 1066 are 3, 4, 9, 27, 52, 79, 164, 237, 711. The anti-divisors which are coprime to 1066 are 3, 9, 27, 79, 237, 711 and their sum is 3 + 9 + 27 + 79 + 237 + 711 = 1066.

Cf. A066272, A066417, A073930, A192270, A240979.

P:=proc(q) local a,k,n;
for n from 3 to q do a:=0; b:=0;
for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then
  if gcd(n,k)=1 then a:=a+k; fi; fi; od;
if n=a then print(n); fi; od; end: P(10^6);

a(14)-a(23) by Jud McCranie, Sep 21 2019.

cp's OEIS Frontend

A192271 Anti-weird numbers.

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A192285 Primitive pseudo anti-perfect numbers.

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A240968 Unitary anti-perfect numbers.

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