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A279585 Partial sums of A279536. 0
0, 0, 1, 3, 8, 11, 12, 12, 21, 21, 22, 41, 42, 42, 63, 63, 64, 74, 75, 75, 79, 79, 80, 80, 80, 83, 83, 83, 84, 152, 153, 153, 153, 158, 158, 158, 159, 159, 163, 163, 164, 189, 190, 190, 193, 193, 194, 194, 194, 197, 197, 197, 205, 205, 205, 210, 210, 210, 211, 223 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..60.

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) = Sum_{h=1..n} ( Sum_{i=3..h} A010051(i) * A010051(2h-i) * ( Sum_{j=i..2h-i} mu(j)^2 ) * (Product_{k=i..h} (1-abs(A010051(k)-A010051(2h-k))))).

MAPLE

with(numtheory): t:=n->add(add( (pi(i)-pi(i-1)) * (pi(2*h-i)-pi(2*h-i-1)) * add(mobius(j)^2, j=i..2*h-i) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*h-k)-pi(2*h-k-1))), k=i..h)), i=3..h), h=1..n): seq(t(n), n=1..60);

CROSSREFS

Cf. A010051, A279536.

Sequence in context: A088072 A213033 A046545 * A108752 A020680 A243169

Adjacent sequences:  A279582 A279583 A279584 * A279586 A279587 A279588

KEYWORD

nonn,easy,changed

AUTHOR

Wesley Ivan Hurt, Dec 15 2016

STATUS

approved

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Last modified February 20 16:25 EST 2018. Contains 299380 sequences. (Running on oeis4.)