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Let  d ( n ) denotes the number of positive integers dividing the positive integer  n , and let  φ ( n ) denotes Euler’s function representing the number of numbers less than and prime to  n . In this paper, we present some notes on the equation  d ( n ) =  d ( φ ( n )). Several results on the related inequalities are also obtained.

Notes on the Equation d ( n ) = d ( φ ( n )) and Related Inequalities