[math-fun] Puzzle

For n in Z+, let q(n) := the total number of prime factors n has (distinct or not) = sum of the exponents in n's prime factorization. Let Zeta_q(s) := Sum{n=1..oo} (-1)^q(n)/(n^s) for Re(s) > 1. Let Zeta_sqf(s) := Sum{n=1..oo, n squarefree} 1/(n^s) for Re(s) > 1. Puzzle: Prove: Zeta_q(s) = Zeta_sqf(s) (for Re(s) > 1). (Don't worry about convergence.) (Note: A := B just signifies that A will stand for B.) --Dan