I think that should be Zeta_q(s) = 1/Zeta_sqf(s). Franklin T. Adams-Watters -----Original Message----- From: dasimov@earthlink.net 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)

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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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun ___________________________________________________ Try the New Netscape Mail Today! Virtually Spam-Free | More Storage | Import Your Contact List http://mail.netscape.com