Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  228.10033
Autor:  Erdös, Paul; Subbarao, M.V.
Title:  On the iterates of some arithmetic functions. (In English)
Source:  Theory arithmetic Functions, Proc. Conf. Western Michigan Univ. 1971, Lecture Notes Math. 251, 119-125 (1972).
Review:  [For the entire collection see Zbl 226.10001.]
Denote by \sigma (n) the sum of the divisors of n and by \sigma^*(n) = prodp\alpha| n (p\alpha+1). The authors prove that for almost all n \sigma (\sigma (n))/n ––> oo but for almost all n \sigma^*(\sigma^*(n))/n remains bounded in fact \sigma^*(\sigma^*(n)) = (1+0(1)) \sigma^*(n). Several related results are proved and some unsolved problems are stated.
Classif.:  * 11N37 Asymptotic results on arithmetic functions
                   11A25 Arithmetic functions, etc.
Citations:  Zbl 226.10001(EA)

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