(OEIS A175639), where the product is over the primes .
Taking the logarithm, expand the sum about infinity, and then summing the terms gives
a "closed" form as
(3)
(4)
where
is the prime zeta function and the s are rational numbers given as the coefficients of in the series
Finch, S. "Class Number Theory." http://algo.inria.fr/csolve/clss.pdf. May 6, 2005.Sloane, N. J. A. Sequence A175639
in "The On-Line Encyclopedia of Integer Sequences."Taniguchi,
T. "A Mean Value Theorem for the Square of Class Number Times Regulator of Quadratic
Extensions." http://arxiv.org/abs/math/0410531.
3 Jul 2006.
![product_(p)[1-3/(p^3)+2/(p^4)+1/(p^5)-1/(p^6)]](/images/equations/TaniguchisConstant/Inline3.svg)
.
Taking the logarithm, expand the sum about infinity, and then summing the terms gives
a "closed" form as
![exp[sum_(n=3)^(infty)c_nP(n)]](/images/equations/TaniguchisConstant/Inline10.svg)
![exp[-3P(3)+2P(4)+P(5)-(11)/2P(6)+6P(7)+...],](/images/equations/TaniguchisConstant/Inline13.svg)
is the prime zeta function and the 
s are rational numbers given as the coefficients of 
in the series
