Ming Shun Yang, Ya Juan Tu
Abstract
Let n be any positive integer, Pd(n)denotes the produce of all positive divisors of n. Let p be a prime, ap(n)denotes the largest exponent (of power p) such that divisible by n. In this paper, we shall use the elementary methods to study the mean value properties of ap(Pd(n)), and give an interesting asymptotic formula for it.
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Let n be any positive integer, Pd(n)denotes the produce of all positive divisors of n. Let p be a prime, ap(n)denotes the largest exponent (of power p) such that divisible by n. In this paper, we shall use the elementary methods to study the mean value properties of ap(Pd(n)), and give an interesting asymptotic formula for it.
Key concepts: Arithmetic function, Divisor function, Mathematics, Exponent, Divisor (algebraic geometry), Integer (computer science), Asymptotic formula, Product (mathematics)