$$\prod_{n=2}^\infty \zeta(n)=2.294856591673313794183$$
Is there a name for this constant, and what are some if its properties?
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9Apparently it gives the average number of abelian groups of a given order. And apparently this is "well-known". http://people.mpim-bonn.mpg.de/zagier/files/tex/ECRH/ECRH.pdf – David H Dec 20 '13 at 01:55
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5OEIS and WMW. – Lucian Dec 20 '13 at 02:44
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1I don't think you can find closed form, since $\sum_{n=2}^\infty \log \zeta(ns) = \sum_p \sum_{m=1}^\infty p^{-sm} (\sigma_{-1}(m)-\frac{1}{m})$. The only hope I see is transforming it into a contour integral, and finding a trick. – reuns Sep 17 '16 at 15:49