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

1,1

Comments

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

Links

Table of n, a(n) for n=1..87.

Example

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.

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

Crossrefs

Cf. A006037, A066272, A192268, A192270.

Sequence in context: A296710 A297143 A138595 * A214423 A185300 A097932

Adjacent sequences: A192268 A192269 A192270 * A192272 A192273 A192274

Keyword

nonn

Author

Paolo P. Lava, Jun 28 2011

Status

approved