Abstract :
We begin by defining a function w on the setimage where pi is prime and pi≠pj for i≠j. If nset membership, variantA3 then was can write n=pqr where p, q, r are primes and possibly two, but not all three of them are equal. For any positive integer m, let P(m) be its largest prime factor. Define the function w on A3 byw(n)=w(pqr)=P(p+q)P(p+r)P(q+r). Our goal is to study the dynamics of w. One of our main results is that every element of A3 is periodic with period a cyclic permutation of the period of 20.
