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Found problems: 1

2004 AMC 10, 24
Let $a_1, a_2, \cdots$, be a sequence with the following properties. I. $a_1 = 1$, and II. $a_{2n}=n\cdot a_n$ for any positive integer $n$. What is the value of $a_{2^{100}}$? $ \textbf{(A)}\; 1\qquad \textbf{(B)}\; 2^{99}\qquad \textbf{(C)}\; 2^{100}\qquad \textbf{(D)}\; 2^{4950}\qquad \textbf{(E)}\; 2^{9999} $
easiest p24 number theory sequences