Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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
     

   Subscribe/Renew Journal


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.
User
Subscription Login to verify subscription
Notifications
Font Size

Abstract Views: 229

PDF Views: 1




  • On the Number of Factorizations of an Integer

Abstract Views: 229  |  PDF Views: 1

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.