The tidbit below is extracted from a post by Victor Miller that got caught in the mailing list filter. The Cohen paper is a good manual for computing zeta-ish products. http://www.math.u-bordeaux.fr/~cohen/hardylw.dvi I also liked the Niklasch paper mentioned in Veit Elser's note. http://oeis.org/A001692/a001692.html "Some number-theoretical constants arising as products of rational functions of p over primes" (Niklasch). Unfortunately, the internal link explaining details is broken. P. Moree, Approximation of singular series and automata, to appear in Manuscripta Math. (1999); preprint available (DVI). http://web.inter.NL.net/hcc/J.Moree/wrench.dvi Rich PS: reminder: the mailing list is configured to drop attachments, and to detain messages over 40KB. ----- Date: Sat, 4 Feb 2012 11:09:11 -0500 Subject: Re: [math-fun] number theory puzzle about squarefree number density From: Victor Miller <victorsmiller@gmail.com> To: math-fun <math-fun@mailman.xmission.com> As Warren pointed out the Euler product converges *really* slowly. That's why I didn't give a numeric value. However, you should look at Henri Cohen's unpublished (it certainly deserves to be published) paper on "High Precision computation of Hardy-Littlewood Constants" http://www.math.u-bordeaux.fr/~cohen/hardylw.dvi which deals with how to get very accurate approximations to such Euler products. It is (not surprisingly) implement in pari, I believe as the function eulerprod. I don't know why the IT newsletter was unreadable. Attached is the page with Golomb's column. Victor