In this article we study the distribution of certain subsets of quadratfrei numbers.

No abstract

We prove a theorem on the distribution of certain sets of composite numbers. The proof use as main lemma a result of the author on the distribution of certain sets of quadratfrei numbers. After, we define the arithmetical function a(n), where a(n) is the number of primes with multiplicity (or exponent) 1 in the prime factorization of n and prove using the previous results on composite numbers that its normal order is log log n. Also, using the previous results on composite numbers, we obtain a theorem on the kernel function and as corollary we obtain that the ABC conjecture holds for almost all C. Mathematics Subject Classification: 11A99, 11B99

In this note we give a simple proof of the well-known result that the square-free numbers have density 6 ∕ π2.

In this note we obtain asymptotic formulae for the square root of the n-th perfect power.