On numbers not of the form \(n-\omega(n)\) (Q812805)

The author proves that there exist infinitely many positive integers \(m\) not of the form \(n-\omega(n)\) for any positive integer \(n\). In this case \(\omega(n)\) is the number of distinct prime factors of \(n\). A similar result holds with \(\omega(n)\) replaced by the total number of prime factors of \(n\) or by the number of divisors of \(n\).