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

Author

Paolo P. Lava, Jun 28 2011

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A006037, A066272, A192268, A192270.

Programs

Maple

# 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