Selberg, Sigmund On the number of positive integers \(\leq x\) containing no isolated prime factors. (Norwegian. English summary) Zbl 0649.10031 Normat 36, No. 1, 1-3 (1988). Author’s summary: “A prime factor p of the natural number n is called isolated if n is divisible by p but not by \(p^ 2\). The author gives an upper and a lower bound for the number A(x) of positive integers \(\leq x\) containing no isolated prime factors: \[ (\zeta (\frac{3}{2})/\zeta (3))x^{1/2}-3x^{1/3}-1\leq A(x)<(\zeta (\frac{3}{2})/\zeta (3))x^{1/2}. \] The proof is short and elementary.” Reviewer: M.Jutila MSC: 11N05 Distribution of primes Keywords:counting function; upper and lower bound; isolated prime factors PDFBibTeX XMLCite \textit{S. Selberg}, Normat 36, No. 1, 1--3 (1988; Zbl 0649.10031)