A279617 Partial sums of A279481.

0, 0, 1, 3, 7, 9, 14, 22, 28, 37, 50, 62, 76, 86, 98, 110, 134, 156, 165, 185, 209, 236, 265, 303, 339, 363, 402, 431, 464, 507, 531, 589, 647, 664, 716, 776, 829, 892, 972, 1018, 1072, 1159, 1229, 1275, 1375, 1437, 1495, 1582, 1613, 1692, 1796, 1867, 1954

Offset

1,4

Links

Table of n, a(n) for n=1..53.

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) = -1 + Sum_{k=1..n} (Sum_{i=2..k} A010051(i) * A010051(2k-i) * (pi(2k-i)-pi(i-1))) for n > 2.

Maple

with(numtheory): A279617:=n->-1+add(add( (pi(i)-pi(i-1)) * (pi(2*k-i)-pi(2*k-i-1)) * (pi(2*k-i)-pi(i-1)), i=2..k), k=1..n): 0, 0, seq(A279617(n), n=3..100);

Crossrefs

Cf. A279481.

Sequence in context: A166733 A172987 A118556 * A199919 A346303 A391741

Adjacent sequences: A279614 A279615 A279616 * A279618 A279619 A279620

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 15 2016

Status

approved