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Reciprocals of Certain Large Additive Functions

Published online by Cambridge University Press:  20 November 2018

J.-M. De Koninck ,
P. Erdös  and
A. Ivić
J.-M. De Koninck
Affiliation:
Département de Mathématiques, Université Laval, Québec GIK 7P4, Canada
P. Erdös
Affiliation:
Hungarian Academy of Sciences Budapest, Hungary
A. Ivić
Affiliation:
Rudarsko-Geoloski Fakultet Universiteta u Beogradu Djusina7, 11000, Beograd Yugoslavia
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Let β(n) = ∑p|nP and B(n) = ∑Pα||nαP denote the sum of distinct prime divisors of n and the sum of all prime divisors of n respectively. Both β(n) and B(n) are additive functions which are in a certain sense large (the average order of B(n) is π2n/(6 log n), [1]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 225 - 231
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Alladi, K. and Erdös, P., On an additive arithmetic function, Pacific J. Math.. 71 (1977), 275-294.Google Scholar
2. de Bruijn, N. G., On the number of positive integers ≤x and free of prime factors >y, Indag. Math.. 13 (1951), 50-60.y,+Indag.+Math..+13+(1951),+50-60.>Google Scholar
3. De Koninck, J.-M., On a class of arithmetical functions, Duke Math. J.. 39 (1972), 807-818.Google Scholar
4. De Koninck, J.-M., Sums of quotients of additive functions, Proc. Amer. Math. Soc. 44 (1974), 35-38.Google Scholar
5. De Koninck, J.-M. and Ivić, A., Sums of reciprocals of certain additive functions, Manuscripta Math.. 30 (1980), 329-341.Google Scholar