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On some Properties of Prime Factors of Integers

Published online by Cambridge University Press:  22 January 2016

P. Erdös
P. Erdös*
Affiliation:
University College, London
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Let A well known theorem of Hardy and Ramanujan states: v(n) = (1 = 0(1))log log n holds for all n if we neglect a sequence of density 0 [5]. Define for 2 ≤j≤v(n)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 617 - 623
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] de Bruijn, N. G., On the number of positive integers ≦x and free of prime factors > y . Indigationes Math., 13 (1945), 50–60.Google Scholar
[2] See, Erdös, E. G. P., On a problem of Chowla and some related problems, Proc. Cambridge Phil. Soc. 32 (1936), p. 532.Google Scholar
[3] Erdös, P., Some remarks on prime factors of integers, Canadian J. Math., 11 (1959), 161–167.Google Scholar
[4] Erdös, P., Some remarks about additive and multiplicative functions, Bull. Amer. Math. Soc., 52 (1946), p. 535 (Theorem 10).Google Scholar
[5] Hardy, G. H. and Ramanujan, S., The normal number of prime factors of n , Quart. J. Math., 48 (1917), 76–92.Google Scholar
[6] Turan, P., On a theorem of Hardy and Ramanujan, J. London Math. Soc., 9 (1934), 274–276.Google Scholar