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Number of prime factors with a given multiplicity
Abstract
Let k ⩾ 1 be a natural number and ωk (n) denote the number of distinct prime factors of a
natural number n with multiplicity k. We estimate the first and second moments of the functions ωk
with k ⩾ 1. Moreover, we prove that the function ω1(n) has normal order log log n and the function
(ω1(n) − log log n)/√log log n has a normal distribution. Finally, we prove that the functions ωk (n)
with k ⩾ 2 do not have normal order F(n) for any nondecreasing nonnegative function F.
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Cite this version of the work
Ertan Elma, Yu-Ru Liu
(2022).
Number of prime factors with a given multiplicity. UWSpace.
http://hdl.handle.net/10012/20007
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