A187619 Sum of the differences of the parts in each Goldbach partition of 2n, A187129(n) - A185297(n).

0, 0, 2, 4, 2, 8, 16, 12, 20, 28, 26, 32, 24, 28, 32, 64, 60, 24, 58, 72, 86, 88, 122, 116, 78, 128, 98, 108, 144, 80, 202, 204, 60, 184, 216, 188, 226, 292, 168, 196, 316, 260, 168, 376, 236, 216, 334, 120, 304, 408, 278, 340, 472, 392, 454, 604, 452, 372, 724, 216, 330, 580, 162, 472, 542, 392, 366, 540, 470, 592, 838, 384, 390, 828

Offset: 2

Author

N. J. A. Sloane, Mar 12 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..1000
• Wikipedia, Goldbach's conjecture
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A226237 (Sum of sums), A045917.

Programs

Maple

with(numtheory):
A279725:=n->2*add( (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * (n-i), i=3..n):
seq(A279725(n), n=1..100); # Wesley Ivan Hurt, Dec 17 2016

Mathematica

Table[2 Sum[(n - i) Floor[2/PrimeOmega[2 n*i - i^2]], {i, 2, n}], {n, 2, 100}] (* Wesley Ivan Hurt, Dec 20 2013 *)

Formula

a(n) = 2 * Sum_{i=2..n} (n-i) * A064911(2*n*i-i^2). - Wesley Ivan Hurt, Dec 20 2013

a(n) = 2 * Sum_{i=3..n} c(i) * c(2*n-i) * (n-i), where c = A010051. - Wesley Ivan Hurt, Dec 17 2016

Extensions

More descriptive name by Wesley Ivan Hurt, Dec 20 2013