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| Title | Shifts of the Prime Divisor Function of Alladi and Erdős |
| Author/s |
Snehal M. Shekatkar
Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411 007 India Tian An Wong Dept. of Mathematics and Statistics, Smith college, Northampton, Massachusetts, USA |
| Abstract | We introduce a variation on the prime divisor function B(n) of Alladiand Erdhos a close relative of the sum of proper divisors function s(n) After proving some basic properties regarding these functions, westudy the dynamics of their iterates and discover behavior that isreminiscent of the aliquot sequences generated by s(n) In particular,we show that for iterates of B(n) njecture. We also discuss possibledirections for further investigation, motivated by numerical observations. |
| Keywords | Iteration, prime numbers, Catalan-Dickson conjecture |
| Download | Journal |
| Citing This Document | Snehal M. Shekatkar, Tian An Wong , Shifts of the Prime Divisor Function of Alladi and Erdős. Technical Report CMS-TR-20200104 of the Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411007, India (2020); available at http://cms.unipune.ac.in/reports/. |
| Notes, Published Reference, Etc. | |
| Contact | snehal.shekatkar@cms.unipune.ac.in |
| Supplementary Material |