V[r_] := DeleteCases[Table[Log[2, x], {x, 1, r}], _Integer]
B[s_] := Sum[
  N[1/(Factorial[Floor[Log[2, s]]]*Delete[V[s], V[s][[n]]])], {n, 1,
   Length[V[s]]}]

0.166667/Delete[{1.58496, 2.32193, 2.58496, 2.80735, 3.16993,
   3.32193}, Key[1.58496]] + 0.166667/
 Delete[{1.58496, 2.32193, 2.58496, 2.80735, 3.16993, 3.32193},
  Key[2.32193]] + 0.166667/
 Delete[{1.58496, 2.32193, 2.58496, 2.80735, 3.16993, 3.32193},
  Key[2.58496]] + 0.166667/
 Delete[{1.58496, 2.32193, 2.58496, 2.80735, 3.16993, 3.32193},
  Key[2.80735]] + 0.166667/
 Delete[{1.58496, 2.32193, 2.58496, 2.80735, 3.16993, 3.32193},
  Key[3.16993]] + 0.166667/
 Delete[{1.58496, 2.32193, 2.58496, 2.80735, 3.16993, 3.32193},
  Key[3.32193]]