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A279792 Number of Goldbach partitions (p,q) of 2n such that 0 < |p-q| < n.

%I A279792 #19 Feb 16 2025 08:33:38
%S A279792 0,0,0,1,1,1,0,1,2,1,0,2,1,1,2,1,1,2,0,2,3,1,1,2,2,1,2,1,1,4,1,2,3,1,
%T A279792 2,3,1,2,2,1,2,4,0,2,5,1,1,3,2,3,4,3,1,4,3,3,5,2,1,6,1,2,5,1,3,4,2,2,
%U A279792 4,4,3,6,3,3,7,2,4,6,1,4,5,2,2,5,4,3,5,3,2,6
%N A279792 Number of Goldbach partitions (p,q) of 2n such that 0 < |p-q| < n.
%H A279792 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A279792 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A279792 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A279792 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A279792 a(n) = Sum_{i=3..n-1} A010051(i) * A010051(2n-i) * sign(floor(n/(2*(n-i)))).
%p A279792 with(numtheory): A279792:=n->add( (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * signum(floor(n/(2*(n-i)))), i=3..n-1): seq(A279792(n), n=1..100);
%t A279792 Table[Sum[Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]] Sign@ Floor[n/(2 (n - i))], {i, 3, n - 1}], {n, 90}] (* _Michael De Vlieger_, Dec 21 2016 *)
%Y A279792 Cf. A010051, A002375, A279794.
%K A279792 nonn,easy
%O A279792 1,9
%A A279792 _Wesley Ivan Hurt_, Dec 18 2016