ON THE MULTIPLICATIVE PARTITION FUNCTION
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 1
Abstract
We study the number of representations n=s1⋯sm, where sj are sonor numbers, i.e. for every sj there do not exist the natural numbers n and k such that sj=nk, k⩾2. The counting function f(n) of such representation is the multiplicative analogue of the additive partitions of n. We construct the asymptotic formula for summatory function of f(n) and investigate the distribution of values of the generalized divisor function L(n) (as the number of representations n factoring two sonor numbers).
Authors and Affiliations
A. Korchevskiy, Ya. Vorobyov
Keywords
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- EP ID EP558772
- DOI 10.18524/2519-206x.2018.1(31).134626
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