

A279728


Sum of the larger parts of the Goldbach partitions (p,q) of 2n such that all primes from p to q (inclusive) appear as a part in some Goldbach partition of p+q = 2n.


5



0, 0, 3, 5, 12, 7, 7, 0, 24, 0, 11, 49, 13, 0, 59, 0, 17, 42, 19, 0, 23, 0, 23, 0, 0, 29, 0, 0, 29, 199, 31, 0, 0, 37, 0, 0, 37, 0, 41, 0, 41, 143, 43, 0, 47, 0, 47, 0, 0, 53, 0, 0, 112, 0, 0, 59, 0, 0, 59, 128, 61, 0, 0, 67, 0, 0, 67, 0, 71, 0, 71, 73, 73, 0, 0, 79, 0, 0
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..78.
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_{i=3..n} ((2ni) * A010051(i) * A010051(2ni) * (Product_{k=i..n} (1abs(A010051(k)A010051(2nk))))).


MAPLE

with(numtheory): A279728:=n>add( (2*ni) * (pi(i)pi(i1)) * (pi(2*ni)pi(2*ni1)) * (product(1abs((pi(k)pi(k1))(pi(2*nk)pi(2*nk1))), k=i..n)), i=3..n): seq(A279728(n), n=1..100);


MATHEMATICA

Table[Sum[((2 n  i) Boole[PrimeQ@ i] Boole[PrimeQ[2 n  i]]) Product[1  Abs[Boole[PrimeQ@ k]  Boole[PrimeQ[2 n  k]]], {k, i, n}], {i, 3, n}], {n, 100}] (* Michael De Vlieger, Dec 18 2016 *)


CROSSREFS

Cf. A010051, A279315, A279727, A279729.
Sequence in context: A101315 A320433 A066541 * A087122 A286900 A037221
Adjacent sequences: A279725 A279726 A279727 * A279729 A279730 A279731


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Dec 17 2016


STATUS

approved



