Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  186.35804
Autor:  Erdös, Pál; Katai, I.
Title:  On the sum sum d4(n) (In English)
Source:  Acta Sci. Math. 30, 313-324 (1969).
Review:  Let d(n) denote the number of divisors of n, and dk(n) be the k-fold iterate of d(n), i. e. d1(n) = d(n) and dk(n) = d(dk-1(n)) for k \geq 2. It was conjectured by Bellman and Shapiro that the relation

sumn \leq k dk(n) = ck(1+o(1))x logkx

holds, where logk denotes the k-fold iterate of logarithm function. This was proved previously for k = 2 by the authors independently, for k = 3 by Kátai. Here the authors prove the case k = 4. The cases k \geq 5 seem to be very difficult.
Classif.:  * 11N37 Asymptotic results on arithmetic functions
Index Words:  number theory

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