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Distribution of the Number of Factors in Random Ordered Factorizations of Integers

โœ Scribed by Hsien-Kuei Hwang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
289 KB
Volume
81
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

We study in detail the asymptotic behavior of the number of ordered factorizations with a given number of factors. Asymptotic formulae are derived for almost all possible values of interest. In particular, the distribution of the number of factors is asymptotically normal. Also we improve the error term in Kalma r's problem of ``factorisatio numerorum'' and investigate the average number of district factors in a random ordered factorization.

2000 Academic Press 1 n x a(n), where n 1 a(n) n &s =(2&(s)) &1 , being Riemann's zeta function; thus a(1)=1 and for n 2 a(n) denotes the number of ordered factorizations of n into 2, 3, 4, ..., namely, the number of different ordered sequences (n 1 , n 2 , ..., n j ) such that n 1 , n 2 , ..., n j 2 and n 1 n 2 } } } n j =n.

We first observe that there exists a \ # (1, 2) such that `( )=2. Numerically, =1.72864 72389+. The function

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