A279726 - OEIS

%I #19 Feb 07 2018 03:07:38

%S 0,0,0,2,6,8,16,32,44,64,92,118,150,174,202,234,298,358,382,440,512,

%T 598,686,808,924,1002,1130,1228,1336,1480,1560,1762,1966,2026,2210,

%U 2426,2614,2840,3132,3300,3496,3812,4072,4240,4616,4852,5068,5402,5522,5826,6234,6512

%N Partial sums of A187619.

%H Vincenzo Librandi, <a href="/A279726/b279726.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = 2 * Sum_{k=1..n} (Sum_{i=3..k} A010051(i) * A010051(2k-i) * (k-i)).

%p 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 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 Cf. A010051, A045917.

%K nonn,easy

%O 1,4

%A _Wesley Ivan Hurt_, Dec 17 2016