Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  188.34102
Autor:  Erdös, Pál; Katai, I.
Title:  On the growth of dk(n) (In English)
Source:  Fibonacci Q. 7, 267-274 (1969).
Review:  Let dk(n) denote the k-fold iterated d(n), where d(n) the number of divisors of n. Let lk be the k-th element of the Fibonacci sequence (l-1 = 0, l0 = 1, lk = lk-1+lk-2, k \geq 2). We prove dk(n) < \exp (log n)1/lk+\epsilon for all fixed k, all positive \epsilon and all sufficiently large values of n; further for every \epsilon > 0 dk(n) > \exp (log n)1/lk-\epsilon for an infinity of values of n. For n > 1 let k(n) denote the smallest k for which dk(n) = 2. We prove

0 < limsup (k(n)/ log log log n) < oo.

Classif.:  * 11N56 Rate of growth of arithmetic functions
Index Words:  number theory

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