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A279726 Partial sums of A187619.

%I A279726 #20 Feb 16 2025 08:33:38
%S A279726 0,0,0,2,6,8,16,32,44,64,92,118,150,174,202,234,298,358,382,440,512,
%T A279726 598,686,808,924,1002,1130,1228,1336,1480,1560,1762,1966,2026,2210,
%U A279726 2426,2614,2840,3132,3300,3496,3812,4072,4240,4616,4852,5068,5402,5522,5826,6234,6512
%N A279726 Partial sums of A187619.
%H A279726 Vincenzo Librandi, <a href="/A279726/b279726.txt">Table of n, a(n) for n = 1..1000</a>
%H A279726 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A279726 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A279726 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A279726 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A279726 a(n) = 2 * Sum_{k=1..n} (Sum_{i=3..k} A010051(i) * A010051(2k-i) * (k-i)).
%p A279726 with(numtheory): a:=n->2*add(add( (pi(i)-pi(i-1)) * (pi(2*k-i)-pi(2*k-i-1)) * (k-i), i=3..k), k=1..n): seq(a(n), n=1..100);
%t A279726 Accumulate@ Table[2 Sum[Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]] (n - i), {i, 3, n}], {n, 56}] (* _Michael De Vlieger_, Dec 17 2016 *)
%Y A279726 Cf. A010051, A045917.
%K A279726 nonn,easy
%O A279726 1,4
%A A279726 _Wesley Ivan Hurt_, Dec 17 2016