This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269801 #21 Mar 17 2016 04:23:13
%S A269801 0,0,0,0,6,7,8,9,10,11,24,0,14,15,32,17,36,0,40,21,44,23,72,0,78,27,
%T A269801 84,0,60,0,96,33,68,35,144,0,152,0,80,41,126,0,176,45,138,47,192,0,
%U A269801 250,51,208,0,162,0,280,57,174,0,240,0,372,63,192,65,330,0
%N A269801 Total sum of the divisors of the primes p,q such that n=p+q and p>=q.
%F A269801 a(n) = (n+2) * A061358(n).
%F A269801 a(n) = (n+2) * Sum_{i=2..floor(n/2)} A010051(i) * A010051(n-i).
%F A269801 a(n) = Sum_{i=2..floor(n/2)} (A000203(i) + A000203(n-i)) * A010051(i) * A010051(n-i).
%e A269801 a(5) = 7; Since 5 can be expressed in one way as the sum of the two primes 2 and 3, we add the sum of their divisors separately: sigma(2) + sigma(3) = 3 + 4 = 7.
%e A269801 a(10) = 24; Since 10 can be expressed in two ways as the sum of two primes, we add the sum of the divisors of each prime p and q: 10 = 3+7 = 5+5, so sigma(3) + sigma(7) + sigma(5) + sigma(5) = 4 + 8 + 6 + 6 = 24.
%p A269801 with(numtheory): A269801:=n->(n+2)*sum((pi(i)-pi(i-1))*(pi(n-i)-pi(n-i-1)), i=2..floor(n/2)): seq(A269801(n), n=0..100);
%t A269801 Table[(n+2) Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, 2, Floor[n/2]}], {n, 0, 80}]
%o A269801 (PARI) a(n) = sum(i=0, n\2, if (isprime(i) && isprime(n-i), sigma(i)+sigma(n-i))); \\ _Michel Marcus_, Mar 05 2016
%Y A269801 Cf. A000203 (sigma), A010051, A014092, A061358.
%K A269801 nonn,easy
%O A269801 0,5
%A A269801 _Wesley Ivan Hurt_, Mar 05 2016