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%I #13 Jun 23 2015 23:00:20
%S 1,3,2,12,96,1152,2304,41472,165888,3981312,119439360,3822059520,
%T 7644119040,321052999680,1284211998720,61642175938560,
%U 3328677500682240,199720650040934400,399441300081868800,1597765200327475200,115039094423578214400,230078188847156428800,18406255107772514304000
%N Numerator of product_{k=1..n-1} (1 + 1/prime(k)).
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979; Theorem 429.
%H Vincenzo Librandi, <a href="/A236435/b236435.txt">Table of n, a(n) for n = 1..200</a>
%H J. Sondow and E. Weisstein, <a href="http://mathworld.wolfram.com/MertensTheorem.html">MathWorld: Mertens Theorem</a>
%F a(n+1) / A236436(n+1) = A072045(n)/A072044(n) / A038110(n+1)/A060753(n+1) because 1+x = (1-x^2) / (1-x).
%F a(n) / A236436(n) = product_{k=1..n-1} (1 + 1/prime(k)) ~ (6/Pi^2)*exp(gamma)*log(n) as n -> infinity, by Mertens' theorem.
%e (1 + 1/2)*(1 + 1/3)*(1 + 1/5)*(1 + 1/7) = 96/35 has numerator a(5) = 96.
%t Numerator@Table[ Product[ 1 + 1/Prime[ k], {k, 1, n-1}], {n, 1, 23}]
%Y Cf. A038110, A060753, A072044, A072045, A236436.
%K nonn,frac
%O 1,2
%A _Jonathan Sondow_, Feb 01 2014
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