AMC 10A 2004 Problem 24

Let a_{1}, a_{2},... , be a sequence with the following properties.

(i) a_{1}=1, and

(ii) a_{2 n}=n.a_{n} for any positive integer n.

What is the value of a_{2^{100}} ?

Answer Choices
A. 1
B. 2^{99}
C. 2^{100}
D. 2^{4950}
E. 2^{9999}