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

1,4

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

Formula

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

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 *)

Crossrefs

Cf. A010051, A045917.

Sequence in context: A191822 A238549 A237502 * A337881 A331974 A137848

Adjacent sequences: A279723 A279724 A279725 * A279727 A279728 A279729

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 17 2016

Status

approved