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On the number of positive integers \(\leq x\) containing no isolated prime factors. (Norwegian. English summary) Zbl 0649.10031

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
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