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%I #13 Oct 06 2017 12:08:39
%S 1,10,101,187,149,1021,33016,6845,37447,343471,217843,269387,652735,
%T 658741,84404851,594869,99801,19571431,845870737,6799977641,
%U 826494610001,4703352797483,5311077568679,5955647363593,5974287995603,2396798638405,2403189712237
%N Numerators of Sum_{n>=1} 1/A045542(n).
%C Goldbach-Euler: sum a(n)/A214391(n) -> 1, n -> oo.
%H Reinhard Zumkeller, <a href="/A214390/b214390.txt">Table of n, a(n) for n = 1..1000</a>
%H L. Bibiloni, P. Viader, and J. Paradis, <a href="https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/bibiloni206.pdf">On a Series of Goldbach and Euler</a>, Amer. Math. Monthly, 113 (2006), pp. 206-220.
%e . n a(n) / A214391(n)
%e . ----------------------------
%e . 1 3.0
%e . 10 1.1827024697863866
%e . 100 1.0142002275801738
%e . 1000 1.0011756130379812 .
%o (Haskell)
%o import Data.Ratio ((%), numerator)
%o a214390 n = a214390_list !! (n-1)
%o a214390_list = map numerator $ scanl1 (+) $ map (1 %) a045542_list
%Y Cf. A214391 (denominators).
%K nonn,frac
%O 1,2
%A _Reinhard Zumkeller_, Jul 15 2012