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Partial sums of A279481.
1

%I #13 Feb 09 2018 03:27:08

%S 0,0,1,3,7,9,14,22,28,37,50,62,76,86,98,110,134,156,165,185,209,236,

%T 265,303,339,363,402,431,464,507,531,589,647,664,716,776,829,892,972,

%U 1018,1072,1159,1229,1275,1375,1437,1495,1582,1613,1692,1796,1867,1954

%N Partial sums of A279481.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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.

%p 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);

%Y Cf. A279481.

%K nonn,easy

%O 1,4

%A _Wesley Ivan Hurt_, Dec 15 2016