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Technical Report CMS-TR-20200104


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
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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
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