A279615 - OEIS

%I #18 Feb 16 2025 08:33:38

%S 0,0,1,3,7,9,10,10,16,16,17,29,30,30,42,42,43,49,50,50,52,52,53,53,53,

%T 55,55,55,56,86,87,87,87,89,89,89,90,90,92,92,93,105,106,106,108,108,

%U 109,109,109,111,111,111,115,115,115,117,117,117,118,124,125,125,125,127,127,127,128,128,130,130,131,133,134

%N Partial sums of A279315.

%H Eric Weisstein's World of Mathematics, <a href="https://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) = Sum_{h=1..n} (Sum_{i=3..h} A010051(i) * A010051(2h-i) * (pi(2h-i)-pi(i-1)) * (Product_{k=i..h} 1-abs(A010051(k)-A010051(2h-k)))).

%p with(numtheory): a:=n->add(add( (pi(i)-pi(i-1)) * (pi(2*h-i)-pi(2*h-i-1)) * (pi(2*h-i)-pi(i-1)) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*h-k)-pi(2*h-k-1))), k=i..h)), i=3..h), h=1..n): seq(a(n), n=1..80);

%Y Cf. A010051, A279315.

%K nonn,easy

%O 1,4

%A _Wesley Ivan Hurt_, Dec 15 2016