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A187619 Sum of the differences of the parts in each Goldbach partition of 2n, A187129(n) - A185297(n).

%I A187619 #23 Apr 30 2021 12:37:05
%S A187619 0,0,2,4,2,8,16,12,20,28,26,32,24,28,32,64,60,24,58,72,86,88,122,116,
%T A187619 78,128,98,108,144,80,202,204,60,184,216,188,226,292,168,196,316,260,
%U A187619 168,376,236,216,334,120,304,408,278,340,472,392,454,604,452,372,724,216,330,580,162,472,542,392,366,540,470,592,838,384,390,828
%N A187619 Sum of the differences of the parts in each Goldbach partition of 2n, A187129(n) - A185297(n).
%H A187619 Vincenzo Librandi, <a href="/A187619/b187619.txt">Table of n, a(n) for n = 2..1000</a>
%H A187619 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A187619 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F A187619 a(n) = 2 * Sum_{i=2..n} (n-i) * A064911(2*n*i-i^2). - _Wesley Ivan Hurt_, Dec 20 2013
%F A187619 a(n) = 2 * Sum_{i=3..n} c(i) * c(2*n-i) * (n-i), where c  = A010051. - _Wesley Ivan Hurt_, Dec 17 2016
%p A187619 with(numtheory):
%p A187619 A279725:=n->2*add( (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * (n-i), i=3..n):
%p A187619 seq(A279725(n), n=1..100); # _Wesley Ivan Hurt_, Dec 17 2016
%t A187619 Table[2 Sum[(n - i) Floor[2/PrimeOmega[2 n*i - i^2]], {i, 2, n}], {n, 2, 100}] (* _Wesley Ivan Hurt_, Dec 20 2013 *)
%Y A187619 Cf. A226237 (Sum of sums), A045917.
%K A187619 nonn
%O A187619 2,3
%A A187619 _N. J. A. Sloane_, Mar 12 2011
%E A187619 More descriptive name by _Wesley Ivan Hurt_, Dec 20 2013