Let d(n)denote the number of positive integers that divide the interger n, including 1 and n. For example, d(1)=1,d(2)=2,and d(12)=6. (This function is known as the divisor function.) Let f(n)=d(n)/n^(1/5). Please find the integer N which makes f(N)=max(f(n)). Let f be a function defined on the set of positive rational numbers with the property that f(a*b)=f(a)+f(b) for all positive rational numbers a and b. Furthermore, suppose that f also has the property that f(p)=p for every prime number p. For which of the following numbers x is f(x)<0? (A)17/32, (B)11/16, (C)7/9, (D)7/6, (E)25/11 All the roots of polynomial z^6-10z^5+Az^4+Bz^3+Cz^2+Dz+16 are positive integers, possibly repeated. What is the value of B?
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