On Two Unconventional Number Theoretic Functions and on Some Related Problmes

n o o lim sup z f nn) _ oo, lim inf 1 f n(n) < oa ., (3) n-a w-a f (n) = pa, F(n) = max pin a i Sn p«5n<P-11 (a i , a j)=1 where all the prime factors of the a 's are the prime factors of n. Trivially f (n) S F(n) and f (n) = F(n) if n-= p-but f (n) = F(n) is possible for arbitrarily large co(n), we will give the simple proof later Probably there is no simple characterization of the integers for which f (n) = F(n) .