A192271 - OEIS

%I #9 Feb 24 2019 20:40:48

%S 11,12,13,14,15,18,20,21,25,27,28,30,37,40,42,43,46,47,48,50,55,57,58,

%T 62,65,66,75,78,80,84,86,87,90,91,92,93,97,99,100,107,111,113,118,119,

%U 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

%N Anti-weird numbers.

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

%e 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.

%p # see A066272

%p 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:

%p isA192268 := proc(n) A066417(n) > n ; end proc:

%p isA192271 := proc(n) isA192268(n) and not isA192270(n) ; end proc:

%p for n from 1 to 40 do if isA192271(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Jul 04 2011

%Y Cf. A006037, A066272, A192268, A192270.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Jun 28 2011