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

1,4

Links

Table of n, a(n) for n=1..60.

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

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))))).

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);

Crossrefs

Cf. A010051, A279536.

Sequence in context: A213033 A305176 A046545 * A350395 A108752 A310279

Adjacent sequences: A279582 A279583 A279584 * A279586 A279587 A279588

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 15 2016

Status

approved