OFFSET
1,4
COMMENTS
a(n) is even for odd n.
If Goldbach's conjecture is true, a(n) > 0 for all even n > 2.
Sum of the areas of the distinct rectangles with prime length and width such that L + W = n, W <= L. For example, a(16) = 94; the two rectangles are 3 X 13 and 5 X 11, and the sum of their areas is 3*13 + 5*11 = 94. - Wesley Ivan Hurt, Oct 28 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Goldbach Partition
Wikipedia, Goldbach's conjecture
FORMULA
a(n) = Sum_{i=2..n/2} i*(n-i) * A064911(i*(n-i)).
MAPLE
with(numtheory): A243485:=n->add(i*(n-i)*(pi(i)-pi(i-1))*(pi(n-i)-pi(n-i-1)), i=1..floor(n/2)): seq(A243485(n), n=1..100); # Wesley Ivan Hurt, Oct 29 2017
MATHEMATICA
Table[Sum[i*(n - i)*Floor[2/PrimeOmega[i (n - i)]], {i, 2, n/2}], {n,
50}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jun 05 2014
STATUS
approved