  Theorem 1 Let F:N-->R stand for any function which a) $F$ monotonically
weakly increases; b) $F$ tends to infinity; and c) such that $q/F(q)$ tends to
infinity.
  Let Z_F(q) equal the number of divisors of q less than sqrt{F(q)} minus the
number of divisors of q between sqrt{F(q)} and F(q).
  Then, on the average, Z_F(q) equals Euler's constant
  Theorem 2 Fix a in (0,1). Write A for the average number of divisors of n
that lie in (0,sqrt{a n}) minus the number of that lie in (sqrt{a n},a n)$.
Then A= (sum_{i=1}^{\lceil {1-a}/a \rceil} \frac{1}{i}) - ln(1/a).
