Let d(n) be the number of integers less then n which has an odd number of prime factors ( 2,3,5,7,8,11,12,13,17,18...).
How to prove d(n)/n have a limit 1/2?
Is there for all m an n such that $|n-2d(n)|>m$?
Let d(n) be the number of integers less then n which has an odd number of prime factors ( 2,3,5,7,8,11,12,13,17,18...).
How to prove d(n)/n have a limit 1/2?
Is there for all m an n such that $|n-2d(n)|>m$?
You can begin to chase down things by starting at this link.
In particular, for the second question, quite a bit more is known. There is a positive constant $k$ such that $|n-2d(n)|>k\sqrt{n}$ for infinitely many $n$.