On the number of positive integers ≦𝑥 all of whose prime factors are ≦𝑦

Chowla, S.; Briggs, W. E.

doi:10.1090/S0002-9939-1955-0071449-7

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the number of positive integers $\leqq x$ all of whose prime factors are $\leqq y$
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by S. Chowla and W. E. Briggs PDF

Proc. Amer. Math. Soc. 6 (1955), 558-562 Request permission

References

N. G. De Bruijn, On the number of uncancelled elements in the sieve of Eratosthenes, Nederl. Akad. Wetensch., Proc. 53 (1950), 803–812 = Indagationes Math. 12, 247–256 (1950). MR 35785
N. G. de Bruijn, On the number of positive integers $\leq x$ and free of prime factors $>y$, Nederl. Acad. Wetensch. Proc. Ser. A. 54 (1951), 50–60. MR 0046375

Vorlesungen über Zahlentheorie

Some theorems concerning the theory of primes

S. D. Chowla and T. Vijayaraghavan, On the largest prime divisors of numbers, J. Indian Math. Soc. (N.S.) 11 (1947), 31–37. MR 23269