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Dirichlet generating function


I wish to expand the product 
Product[1/(1-n^(-s)),{n,2,12}] to obtain output in the form of a Dirichlet series,
1+2^(-s)+3^(-s)+2*4^(-s)+5^(-s)+2*6^(-s)+...4*12^(-s)+...

(The coefficients of m^(-s) in the above series give the number of
factorizations of m into factors greater than 1. E.g. 12 can be factored
in 4 ways, as 12 or 6*2 or 4*3 or 3*2*2).

Thanks


Arnold Knopfmacher
Dept of Computational and Applied Maths
Witwatersrand University
Johannesburg 2050
South Africa
http://www.wits.ac.za/science/number_theory/arnold.htm
Fax: 2711-4039317
Phone: 2711- 717-6121
email: arnoldk at gauss.cam.wits.ac.za


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