A279585 Partial sums of A279536.

0, 0, 1, 3, 8, 11, 12, 12, 21, 21, 22, 41, 42, 42, 63, 63, 64, 74, 75, 75, 79, 79, 80, 80, 80, 83, 83, 83, 84, 152, 153, 153, 153, 158, 158, 158, 159, 159, 163, 163, 164, 189, 190, 190, 193, 193, 194, 194, 194, 197, 197, 197, 205, 205, 205, 210, 210, 210, 211, 223

Offset: 1

Author

Wesley Ivan Hurt, Dec 15 2016

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Goldbach Partition
• Wikipedia, Goldbach's conjecture
• Index entries for sequences related to Goldbach conjecture
• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A279536.

Programs

Maple

with(numtheory): t:=n->add(add( (pi(i)-pi(i-1)) * (pi(2*h-i)-pi(2*h-i-1)) * add(mobius(j)^2, j=i..2*h-i) * (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(t(n), n=1..60);

Formula

a(n) = Sum_{h=1..n} ( Sum_{i=3..h} A010051(i) * A010051(2h-i) * ( Sum_{j=i..2h-i} mu(j)^2 ) * (Product_{k=i..h} (1-abs(A010051(k)-A010051(2h-k))))).