Journal of the Ramanujan Mathematical Society

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On the Number of Factorizations of an Integer


Affiliations
1 Institute of Mathematical Sciences, Taramani, Chennai, 600 113, India
2 Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400 094, India
     

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Let f (n) denote the number of unordered factorizations of a positive integer n into factors larger than 1. We show that the number of distinct values of f (n), less than or equal to x, is at most exp (C √log x / loglog x (1+o(1))), where C = 2π √ 2/3 and x is sufficiently large. This improves upon a previous result of the first author and F. Luca.
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  • On the Number of Factorizations of an Integer

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Authors

R. Balasubramanian
Institute of Mathematical Sciences, Taramani, Chennai, 600 113, India
Priyamvad Srivastav
Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400 094, India

Abstract


Let f (n) denote the number of unordered factorizations of a positive integer n into factors larger than 1. We show that the number of distinct values of f (n), less than or equal to x, is at most exp (C √log x / loglog x (1+o(1))), where C = 2π √ 2/3 and x is sufficiently large. This improves upon a previous result of the first author and F. Luca.