A279726 Partial sums of A187619.

0, 0, 0, 2, 6, 8, 16, 32, 44, 64, 92, 118, 150, 174, 202, 234, 298, 358, 382, 440, 512, 598, 686, 808, 924, 1002, 1130, 1228, 1336, 1480, 1560, 1762, 1966, 2026, 2210, 2426, 2614, 2840, 3132, 3300, 3496, 3812, 4072, 4240, 4616, 4852, 5068, 5402, 5522, 5826, 6234, 6512

Offset: 1

Author

Wesley Ivan Hurt, Dec 17 2016

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• 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, A045917.

Programs

Maple

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

Mathematica

Accumulate@ Table[2 Sum[Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]] (n - i), {i, 3, n}], {n, 56}] (* Michael De Vlieger, Dec 17 2016 *)

Formula

a(n) = 2 * Sum_{k=1..n} (Sum_{i=3..k} A010051(i) * A010051(2k-i) * (k-i)).