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What is Mean Value Properties of Smarandache Function about?

This document defines and studies the Smarandache multiplicative function f(n). It defines f(n) such that f(ab) = max(f(a), f(b)) for coprime a and b, and f(p^α) = αp for primes p and exponents α. It proves that f(n) gives the greatest prime factor of n if this factor is greater than the square root of n. The main result is a theorem proving an asymptotic formula for the mean value of f(n) as n increases: the mean value is approximately π2x2/ln2x. The proof uses properties of the greatest prime factor, the

Author

RyanElias

Language

EN