
COMMENTS

Comment from N. J. A. Sloane, Mar 10 2011: This is a list of values of 2n such that A185297(n) divides A187129(n).
Comment from T. D. Noe, Mar 10 2011: I have some fast code for counting Goldbach partitions. I made a slight change so that it sums the partitions instead. Using this new program, I did not find any additional terms < 10^7.


EXAMPLE

For 2n=52, the partitions are (5,47), (11,41) and (23,29). The lesser sum of primes is 5+11+23=39 and the greater sum of primes is 29+41+47=117, with 39117 for quotient 3.
For the 2n listed, the values of (s1(n), s2(n)/s1(n)) are (2,1), (3,1), (8,3), (12,2), (10,3), (16,3), (39,3), (108,3), (204,3), (630,3), (35332,3).


MATHEMATICA

okQ[n_] := Module[{p, q}, p = Select[Prime[Range[PrimePi[n]]], PrimeQ[2 n  #] &]; q = 2 n  p; Mod[Plus @@ q, Plus @@ p] == 0]; 2*Select[Range[2, 10000], okQ]
