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%I #9 Sep 22 2012 18:03:57
%S 0,2,5,3,5,7,10,9,8,2,28,16,28,20,26,9,58,22,58,37,56,22,100,28,75,35,
%T 100,44,129,39,129,96,127,41,160,16,197,140,158,77,238,70,238,149,236,
%U 120,328,88,279,128,328,172,381,111,326,213,381,178,440,80,440
%N The sum of the primes less than or equal to n minus the sum of the distinct elements of the Goldbach partitions of n.
%C If n is prime then a(n) sets or equals a record.
%C If n and n+2 are twin primes then a(n) = a(n+2).
%H J. Stauduhar, <a href="/A216052/b216052.txt">Table of n, a(n) for n = 1..10000</a>
%e With n = 2, the sum of the primes <= 2 is 2, and the sum of the distinct elements of the Goldbach partitions of 2 is 0, so a(2) = 2 + 0 = 2.
%e With n = 4, the sum of the primes <= 4 is 5, and the sum of the distinct elements of the Goldbach partitions of is 2, so a(4) = 5 - 2 = 3.
%t f[n_] := Module[{lst={}}, For[i=1, i<=n, i++, t = Plus @@ Select[ Table[Prime[i], {i, PrimePi[i]}], !PrimeQ[i-#]&]; AppendTo[lst, t]]; lst]; f[1000] (* J. Stauduhar, Sep 22 2012 *)
%K nonn
%O 1,2
%A _J. Stauduhar_, Sep 22 2012
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