OFFSET
1,2
COMMENTS
Goldbach's Conjecture states that every positive even integer > 4 is expressible as the sum of two odd primes in at least one way. This is logically equivalent to the statement that a(n) > 0 for n > 2.
The sum of the parts in the partitions of 2n into exactly two prime parts.
LINKS
Eric Weisstein's World of Mathematics, Goldbach Partition
Wikipedia, Goldbach's conjecture
EXAMPLE
a(13) = 78. Since 2*13 = 26 has exactly 3 Goldbach partitions: (23,3),(19,7), and (13,13). The sum of the parts gives: 23+19+13+13+7+3 = 78.
MAPLE
MATHEMATICA
Table[ 2 n*Sum[ Floor[2/PrimeOmega[2 n*i - i^2]], {i, 2, n}], {n,
100}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Aug 25 2013
STATUS
approved